**Preprints**

- C. Avraam and E. Mallada, Voltage Collapse Stabilization in Star DC Networks, 2021, submitted.

[BibTeX] [Abstract] [Download PDF]Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

`@unpublished{am2021a-preprint, abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.}, author = {Avraam, Charalampos and Mallada, Enrique}, author+an = {2=first}, month = {4}, pages = {1-12}, title = {Voltage Collapse Stabilization in Star DC Networks}, url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-AM.pdf}, year = {2021, submitted} }`

- A. Castellano, H. Min, J. Bazerque, and E. Mallada, Learning to Act Safely with Limited Exposure and Almost Sure Certainty, 2021, submitted.

[BibTeX] [Abstract] [Download PDF]This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one is willing to navigate trade-offs between optimality, level of exposure to unsafe events, and the maximum detection time of unsafe actions. We illustrate this concept in two complementary settings. We first focus on the canonical multi-armed bandit problem and seek to study the intrinsic trade-offs of learning safety in the presence of uncertainty. Under mild assumptions on sufficient exploration, we provide an algorithm that provably detects all unsafe machines in an (expected) finite number of rounds. The analysis also unveils a trade-off between the number of rounds needed to secure the environment and the probability of discarding safe machines. We then consider the problem of finding optimal policies for a Markov Decision Process (MDP) with almost sure constraints. We show that the (action) value function satisfies a barrier-based decomposition which allows for the identification of feasible policies independently of the reward process. Using this decomposition, we develop a Barrier-learning algorithm, that identifies such unsafe state-action pairs in a finite expected number of steps. Our analysis further highlights a trade-off between the time lag for the underlying MDP necessary to detect unsafe actions, and the level of exposure to unsafe events. Simulations corroborate our theoretical findings, further illustrating the aforementioned trade-offs, and suggesting that safety constraints can further speed up the learning process.

`@unpublished{cmbm2021a-preprint, abstract = {This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one is willing to navigate trade-offs between optimality, level of exposure to unsafe events, and the maximum detection time of unsafe actions. We illustrate this concept in two complementary settings. We first focus on the canonical multi-armed bandit problem and seek to study the intrinsic trade-offs of learning safety in the presence of uncertainty. Under mild assumptions on sufficient exploration, we provide an algorithm that provably detects all unsafe machines in an (expected) finite number of rounds. The analysis also unveils a trade-off between the number of rounds needed to secure the environment and the probability of discarding safe machines. We then consider the problem of finding optimal policies for a Markov Decision Process (MDP) with almost sure constraints. We show that the (action) value function satisfies a barrier-based decomposition which allows for the identification of feasible policies independently of the reward process. Using this decomposition, we develop a Barrier-learning algorithm, that identifies such unsafe state-action pairs in a finite expected number of steps. Our analysis further highlights a trade-off between the time lag for the underlying MDP necessary to detect unsafe actions, and the level of exposure to unsafe events. Simulations corroborate our theoretical findings, further illustrating the aforementioned trade-offs, and suggesting that safety constraints can further speed up the learning process.}, author = {Castellano, Agustin and Min, Hancheng and Bazerque, Juan and Mallada, Enrique}, month = {5}, pages = {1-16}, title = {Learning to Act Safely with Limited Exposure and Almost Sure Certainty}, url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-CMBM.pdf}, year = {2021, submitted} }`

- H. Min and E. Mallada, Coherence and Concentration in Tightly-Connected Networks, 2021, submitted.

[BibTeX] [Abstract] [Download PDF]Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

`@unpublished{mm2021a-preprint, abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.}, author = {Min, Hancheng and Mallada, Enrique}, grants = {CAREER-1752362;EPCN-1711188;AMPS-1736448;TRIPODS-1934979}, month = {1}, pages = {1-16}, title = {Coherence and Concentration in Tightly-Connected Networks}, url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-MM.pdf}, year = {2021, submitted} }`

- G. H. Oral, E. Mallada, and D. Gayme, On the Role of Interconnection Directionality in the Quadratic Performance of Double-Integrator Networks, 2021, under review.

[BibTeX] [Abstract] [Download PDF]This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of position and velocity based response functions given impulsive inputs to each vehicle. We exploit the spectral properties of weighted graph Laplacians and output performance matrices to derive a novel method of computing the closed-form solutions for this general class of performance metrics, which include H2-norm based quantities as special cases. We then explore the effect of the interplay between network properties (such as edge directionality and connectivity) and the control strategy on the overall network performance. More precisely, for systems whose interconnection is described by graphs with normal Laplacian L, we characterize the role of directionality by comparing their performance with that of their undirected counterparts, represented by the Hermitian part of L. We show that, for single-integrator networks, directed and undirected graphs perform identically. However, for double-integrator networks, graph directionality -expressed by the eigenvalues of L with nonzero imaginary part- can significantly degrade performance. Interestingly, in many cases, well-designed feedback can also exploit directionality to mitigate degradation or even improve the performance to exceed that of the undirected case. Finally we focus on a system coherence metric -aggregate deviation from the state average- to investigate the relationship between performance and degree of connectivity, leading to somewhat surprising findings. For example, increasing the number of neighbors on a ω-nearest neighbor directed graph does not necessarily improve performance. Similarly, we demonstrate equivalence in performance between all-to-one and all-to-all communication graphs.

`@unpublished{omg2021a-preprint, abstract = {This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of position and velocity based response functions given impulsive inputs to each vehicle. We exploit the spectral properties of weighted graph Laplacians and output performance matrices to derive a novel method of computing the closed-form solutions for this general class of performance metrics, which include H2-norm based quantities as special cases. We then explore the effect of the interplay between network properties (such as edge directionality and connectivity) and the control strategy on the overall network performance. More precisely, for systems whose interconnection is described by graphs with normal Laplacian L, we characterize the role of directionality by comparing their performance with that of their undirected counterparts, represented by the Hermitian part of L. We show that, for single-integrator networks, directed and undirected graphs perform identically. However, for double-integrator networks, graph directionality -expressed by the eigenvalues of L with nonzero imaginary part- can significantly degrade performance. Interestingly, in many cases, well-designed feedback can also exploit directionality to mitigate degradation or even improve the performance to exceed that of the undirected case. Finally we focus on a system coherence metric -aggregate deviation from the state average- to investigate the relationship between performance and degree of connectivity, leading to somewhat surprising findings. For example, increasing the number of neighbors on a ω-nearest neighbor directed graph does not necessarily improve performance. Similarly, we demonstrate equivalence in performance between all-to-one and all-to-all communication graphs.}, author = {Oral, H. Giray and Mallada, Enrique and Gayme, Dennice}, grants = {ENERGISE-DE-EE0008006, EPCN-1711188,AMPS-1736448, CPS-1544771, CAREER-1752362, AMPS-1736448, ARO-W911NF-17-1-0092}, month = {4}, pages = {1-8}, record = {revised Nov. 2020, submitted Nov. 2019}, title = {On the Role of Interconnection Directionality in the Quadratic Performance of Double-Integrator Networks}, url = {https://mallada.ece.jhu.edu/pubs/2019-Preprint-OMG.pdf}, year = {2021, under review} }`

- R. Pates, A. Ferragut, E. Pivo, P. You, F. Paganini, and E. Mallada, Respect the Unstable: Delays and Saturation in Contact Tracing for Disease Control, 2020, submitted.

[BibTeX] [Abstract] [Download PDF]Motivated by the novel coronavirus disease (COVID-19) pandemic, this paper aims to apply Gunter Stein’s cautionary message of respecting the unstable to the problem of controlling the spread of an infectious disease. With this goal, we study the effect that delays and capacity constraints in the TeTrIs process have on preventing exponential disease spread. Our analysis highlights the critical importance of speed and scale in the TeTrIs process. Precisely, having a delay in the TeTrIs process smaller than the doubling time of the disease spread is necessary for achieving acceptable performance. Similarly, limited TeTrIs capacity introduces a threshold on the size of an outbreak beyond which the disease spreads almost like the uncontrolled case. Along the way, we provide numerical illustrations to highlight these points.

`@unpublished{pfpypm2021a-preprint, abstract = {Motivated by the novel coronavirus disease (COVID-19) pandemic, this paper aims to apply Gunter Stein's cautionary message of respecting the unstable to the problem of controlling the spread of an infectious disease. With this goal, we study the effect that delays and capacity constraints in the TeTrIs process have on preventing exponential disease spread. Our analysis highlights the critical importance of speed and scale in the TeTrIs process. Precisely, having a delay in the TeTrIs process smaller than the doubling time of the disease spread is necessary for achieving acceptable performance. Similarly, limited TeTrIs capacity introduces a threshold on the size of an outbreak beyond which the disease spreads almost like the uncontrolled case. Along the way, we provide numerical illustrations to highlight these points.}, author = {Pates, Richard and Ferragut, Andres and Pivo, Elijah and You, Pengcheng and Paganini, Fernando and Mallada, Enrique}, grants = {CAREER-1752362, EPCN-1711188, AMPS-1736448, TRIPODS-1934979}, month = {11}, pages = {1-25}, title = {Respect the Unstable: Delays and Saturation in Contact Tracing for Disease Control}, url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-PFPYPM.pdf}, year = {2020, submitted} }`

- T. Zheng, J. Guthrie, and E. Mallada, Tight Inner Approximations of the Positive-Semidefinite Cone via Grassmannian Packings, 2021, submitted.

[BibTeX] [Abstract] [Download PDF]We investigate the problem of finding tight innerapproximations of large dimensional positive semidefinite (PSD)cones. To solve this problem, we develop a novel decompositionframework of the PSD cone by means of conical combinationsof smaller dimensional sub-cones. We show that many innerapproximation techniques could be summarized within thisframework, including the set of (scaled) diagonally dominantmatrices, Factor-widthkmatrices, and Chordal Sparse ma-trices. Furthermore, we provide a more flexible family ofinner approximations of the PSD cone, where we aim toarrange the sub-cones so that they are maximally separatedfrom each other. In doing so, these approximations tend tooccupy large fractions of the volume of the PSD cone. Theproposed approach is connected to a classical packing problemin Riemannian Geometry. Precisely, we show that the problemof finding maximally distant sub-cones in an ambient PSD coneis equivalent to the problem of packing sub-spaces in a Grass-mannian Manifold. We further leverage existing computationalmethod for constructing packings in Grassmannian manifoldsto build tighter approximations of the PSD cone. Numericalexperiments show how the proposed framework can balancebetween accuracy and computational complexity, to efficientlysolve positive-semidefinite programs.

`@unpublished{zgm2021a-preprint, abstract = {We investigate the problem of finding tight innerapproximations of large dimensional positive semidefinite (PSD)cones. To solve this problem, we develop a novel decompositionframework of the PSD cone by means of conical combinationsof smaller dimensional sub-cones. We show that many innerapproximation techniques could be summarized within thisframework, including the set of (scaled) diagonally dominantmatrices, Factor-widthkmatrices, and Chordal Sparse ma-trices. Furthermore, we provide a more flexible family ofinner approximations of the PSD cone, where we aim toarrange the sub-cones so that they are maximally separatedfrom each other. In doing so, these approximations tend tooccupy large fractions of the volume of the PSD cone. Theproposed approach is connected to a classical packing problemin Riemannian Geometry. Precisely, we show that the problemof finding maximally distant sub-cones in an ambient PSD coneis equivalent to the problem of packing sub-spaces in a Grass-mannian Manifold. We further leverage existing computationalmethod for constructing packings in Grassmannian manifoldsto build tighter approximations of the PSD cone. Numericalexperiments show how the proposed framework can balancebetween accuracy and computational complexity, to efficientlysolve positive-semidefinite programs.}, author = {Zheng, Tianqi and Guthrie, James and Mallada, Enrique}, grants = {EPCN-1711188, CAREER-1752362, AMPS-1736448, TRIPODS-1934979}, month = {3}, title = {Tight Inner Approximations of the Positive-Semidefinite Cone via Grassmannian Packings}, url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-ZGM.pdf}, year = {2021, submitted} }`

**Journals**

- Y. Jiang, A. Bernstein, P. Vorobev, and E. Mallada, “Grid-forming frequency shaping control in low inertia power systems,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 6, pp. 1988-1993, 2021. doi:10.1109/LCSYS.2020.3044551

[BibTeX] [Abstract] [Download PDF]We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models –based on frequency weighted balanced truncation– that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.

`@article{jbvm2021lcss, abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.}, author = {Jiang, Yan and Bernstein, Andrey and Vorobev, Petr and Mallada, Enrique}, doi = {10.1109/LCSYS.2020.3044551}, grants = {CAREER-1752362, AMPS-1736448, TRIPODS-1934979, EPCN-1711188}, journal = {IEEE Control Systems Letters (L-CSS)}, month = {12}, note = {also in ACC 2021}, number = {6}, pages = {1988-1993}, record = {early access Dec 2020, accepted Nov 2020, revised Nov 2020, submitted Sep 2020}, title = {Grid-forming frequency shaping control in low inertia power systems}, url = {https://mallada.ece.jhu.edu/pubs/2021-LCSS-JBVM.pdf}, volume = {5}, year = {2021} }`

- H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 5, pp. 1741-1746, 2021. doi:10.1109/LCSYS.2020.3043733

[BibTeX] [Abstract] [Download PDF]We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models –based on frequency weighted balanced truncation– that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.

`@article{mpm2021lcss, abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.}, author = {Min, Hancheng and Paganini, Fernando and Mallada, Enrique}, doi = {10.1109/LCSYS.2020.3043733}, grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092}, journal = {IEEE Control Systems Letters (L-CSS)}, month = {11}, note = {also in ACC 2021}, number = {5}, pages = {1741-1746}, record = {early accesss Nov 2020, accepted Nov 2020, revised Nov 2020, submitted Sep 2020}, title = {Accurate Reduced Order Models for Coherent Heterogeneous Generators}, url = {https://mallada.ece.jhu.edu/pubs/2021-LCSS-MPM.pdf}, volume = {5}, year = {2021} }`

- Y. Jiang, E. Cohn, P. Vorobev, and E. Mallada, “Storage-Based Frequency Shaping Control,” IEEE Transactions on Power Systems, pp. 1-13, 2021. doi:10.1109/TPWRS.2021.3072833

[BibTeX] [Abstract] [Download PDF]With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage — frequency shaping control — that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.

`@article{jcvm2021tps, abstract = {With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage -- frequency shaping control -- that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.}, author = {Jiang, Yan and Cohn, Eliza and Vorobev, Petr and Mallada, Enrique}, doi = {10.1109/TPWRS.2021.3072833}, journal = {IEEE Transactions on Power Systems}, month = {4}, pages = {1-13}, pubstate = {early access}, record = {accepted Mar 2021, revised Oct 2020, submitted May 2020}, title = {Storage-Based Frequency Shaping Control}, url = {https://mallada.ece.jhu.edu/pubs/2021-TPS-JCVM.pdf}, year = {2021} }`

- M. D. Kaba, M. Zhao, R. Vidal, D. R. Robinson, and E. Mallada, “What is the Largest Sparsity Pattern that Can Be Recovered by 1-Norm Minimization?,” IEEE Transactions on Information Theory, vol. 67, iss. 5, pp. 3060-3074, 2021. doi:10.1109/TIT.2021.3067280

[BibTeX] [Abstract] [Download PDF]We propose a new framework for studying the recovery of signals with structured sparsity patterns via $l_1$-minimization. We achieve this by generalizing the well-known nullspace property for sparse recovery. We show that for each dictionary there is a maximum sparsity pattern—described by a mathematical object called an abstract simplicial complex—that can be recovered via $l_1$-minimization. We provide two different characterizations of this maximum sparsity pattern. In addition, we show how this new framework is useful in the study of sparse recovery problems when the dictionary takes the form of a graph incidence matrix or a partial Discrete Fourier Transform. In both cases we successfully characterize the collection of all support sets for which exact recovery via $l_1$-minimization is possible. When the dictionary is an incidence matrix, we show that the success of exact recovery can be certified in polynomial time, although this is known to be NP-hard for general matrices.

`@article{kzvrm2021tit, abstract = {We propose a new framework for studying the recovery of signals with structured sparsity patterns via $l_1$-minimization. We achieve this by generalizing the well-known nullspace property for sparse recovery. We show that for each dictionary there is a maximum sparsity pattern---described by a mathematical object called an abstract simplicial complex---that can be recovered via $l_1$-minimization. We provide two different characterizations of this maximum sparsity pattern. In addition, we show how this new framework is useful in the study of sparse recovery problems when the dictionary takes the form of a graph incidence matrix or a partial Discrete Fourier Transform. In both cases we successfully characterize the collection of all support sets for which exact recovery via $l_1$-minimization is possible. When the dictionary is an incidence matrix, we show that the success of exact recovery can be certified in polynomial time, although this is known to be NP-hard for general matrices.}, author = {Kaba, Mustafa Devrim and Zhao, Mengnan and Vidal, Rene and Robinson, Daniel R. and Mallada, Enrique}, doi = {10.1109/TIT.2021.3067280}, grants = {AMPS:1736448;CAREER-1752362}, journal = {IEEE Transactions on Information Theory}, month = {5}, number = {5}, pages = {3060-3074}, record = {early access Mar. 2021, accepted Jan. 2021, revised Apr. 2020, submitted Oct. 2019}, title = {What is the Largest Sparsity Pattern that Can Be Recovered by 1-Norm Minimization?}, url = {https://mallada.ece.jhu.edu/pubs/2021-TIT-KZVRM.pdf}, volume = {67}, year = {2021} }`

- M. Almassalkhi, S. Brahma, N. Nazir, H. Ossareh, P. Racherla, S. Kundu, S. P. Nandanoori, T. Ramachandran, A. Singhal, D. Gayme, C. Ji, E. Mallada, Y. Shen, P. You, and D. Anand, “Hierarchical, Grid-Aware, and Economically Optimal Coordination of Distributed Energy Resources in Realistic Distribution Systems,” Energies, vol. 13, iss. 23, pp. 1-35, 2020. doi:10.3390/en13236399

[BibTeX] [Abstract] [Download PDF]Forward-looking renewable portfolio standards will lead to extreme levels of variable solar PV in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliablymanage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimize the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.

`@article{abetal2020energies, abstract = {Forward-looking renewable portfolio standards will lead to extreme levels of variable solar PV in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliablymanage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimize the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.}, author = {Almassalkhi, Mads and Brahma, Sarnaduti and Nazir, Nawaf and Ossareh, Hamid and Racherla, Pavan and Kundu, Soumya and Nandanoori, Sai P. and Ramachandran, Thiagarajan and Singhal, Ankit and Gayme, Dennice and Ji, Chengda and Mallada, Enrique and Shen, Yue and You, Pengcheng and Anand, Dhananjay}, doi = {10.3390/en13236399}, grants = {CAREER-1752362,EPCN-1711188,AMPS-1736448,TRIPODS-1934979}, journal = {Energies}, month = {12}, number = {23}, pages = {1-35}, title = {Hierarchical, Grid-Aware, and Economically Optimal Coordination of Distributed Energy Resources in Realistic Distribution Systems}, url = {https://mallada.ece.jhu.edu/pubs/2020-ENERGIES-ABetal.pdf}, volume = {13}, year = {2020} }`

- L. S. P. Lawrence, J. W. Simpson-Porco, and E. Mallada, “Linear-Convex Optimal Steady-State Control,” IEEE Transactions on Automatic Control, pp. 1-8, 2020. doi:10.1109/TAC.2020.3044275

[BibTeX] [Abstract] [Download PDF]We consider the problem of designing a feedback controller for a multivariable nonlinear system that regulates an arbitrary subset of the system states and inputs to the solution of a constrained optimization problem, despite parametric modelling uncertainty and time-varying exogenous disturbances; we term this the optimal steady-state (OSS) control problem. We derive necessary and sufficient conditions for the existence of an OSS controller by formulating the OSS control problem as an output regulation problem wherein the regulation error is unmeasurable. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the OSS control problem to an output regulation problem with measurable error. This yields a design framework for OSS control that unifies and extends many existing designs in the literature. We present a complete and constructive solution of the OSS control problem for the case where the plant is linear time-invariant with structured parametric uncertainty, and disturbances are constant in time. We illustrate these results via an application to optimal frequency control of power networks, and show that our design procedure recovers several frequency controllers from the recent literature.

`@article{lsm2020tac, abstract = {We consider the problem of designing a feedback controller for a multivariable nonlinear system that regulates an arbitrary subset of the system states and inputs to the solution of a constrained optimization problem, despite parametric modelling uncertainty and time-varying exogenous disturbances; we term this the optimal steady-state (OSS) control problem. We derive necessary and sufficient conditions for the existence of an OSS controller by formulating the OSS control problem as an output regulation problem wherein the regulation error is unmeasurable. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the OSS control problem to an output regulation problem with measurable error. This yields a design framework for OSS control that unifies and extends many existing designs in the literature. We present a complete and constructive solution of the OSS control problem for the case where the plant is linear time-invariant with structured parametric uncertainty, and disturbances are constant in time. We illustrate these results via an application to optimal frequency control of power networks, and show that our design procedure recovers several frequency controllers from the recent literature.}, author = {Lawrence, Liam S. P. and Simpson-Porco, John W. and Mallada, Enrique}, doi = {10.1109/TAC.2020.3044275}, journal = {IEEE Transactions on Automatic Control}, month = {12}, pages = {1-8}, pubstate = {early access}, record = {accepted Nov 2020, conditionally accepted Aug. 2020, 2nd revision May 2020, revised Sept 2019, submitted Oct. 2018}, title = {Linear-Convex Optimal Steady-State Control}, url = {https://mallada.ece.jhu.edu/pubs/2020-TAC-LSM.pdf}, year = {2020} }`

- Y. Jiang, R. Pates, and E. Mallada, “Dynamic Droop Control in Low Inertia Power Systems,” IEEE Transactions on Automatic Control, pp. 1-16, 2020. doi:10.1109/TAC.2020.3034198

[BibTeX] [Abstract] [Download PDF]A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the grid’s stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies –droop control (DC) and virtual inertia (VI)– on several performance metrics induced by L2 and L∞ signal norms. By extending a recently proposed modal decomposition method, we capture the effect of step and stochastic power disturbances, and frequency measurement noise, on the overall transient and steady-state behavior of the system. Our analysis unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without increasing steady-state control effort, or the large frequency variance that VI introduces in the presence of measurement noise. We further propose a novel dynam-i-c Droop controller (iDroop) that overcomes the limitations of DC and VI. More precisely, we show that iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or frequency overshoot (Nadir) elimination without affecting the steady-state control effort share, and propose a tuning recommendation that strikes a balance among these objectives. Extensive numerical experimentation shows that the proposed tuning is effective even when our proportionality assumptions are not valid, and that the particular tuning used for Nadir elimination strikes a good trade-off among various performance metrics.

`@article{jpm2020tac, abstract = {A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the grid's stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies --droop control (DC) and virtual inertia (VI)-- on several performance metrics induced by L2 and L∞ signal norms. By extending a recently proposed modal decomposition method, we capture the effect of step and stochastic power disturbances, and frequency measurement noise, on the overall transient and steady-state behavior of the system. Our analysis unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without increasing steady-state control effort, or the large frequency variance that VI introduces in the presence of measurement noise. We further propose a novel dynam-i-c Droop controller (iDroop) that overcomes the limitations of DC and VI. More precisely, we show that iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or frequency overshoot (Nadir) elimination without affecting the steady-state control effort share, and propose a tuning recommendation that strikes a balance among these objectives. Extensive numerical experimentation shows that the proposed tuning is effective even when our proportionality assumptions are not valid, and that the particular tuning used for Nadir elimination strikes a good trade-off among various performance metrics.}, author = {Jiang, Yan and Pates, Richard and Mallada, Enrique}, doi = {10.1109/TAC.2020.3034198}, grants = {ENERGISE-DE-EE0008006, EPCN-1711188,AMPS-1736448, CPS-1544771, CAREER-1752362, AMPS-1736448, ARO-W911NF-17-1-0092}, journal = {IEEE Transactions on Automatic Control}, month = {11}, pages = {1-16}, record = {available online Nov. 2020, accepted Aug. 2020, revised Mar. 2020, submitted Aug. 2019}, title = {Dynamic Droop Control in Low Inertia Power Systems}, url = {https://mallada.ece.jhu.edu/pubs/2020-TAC-JPM.pdf}, year = {2020} }`

- A. Bahram, M. H. Hajiesmaili, Z. Lee, N. Crespi, and E. Mallada, “Online EV Scheduling Algorithms for Adaptive Charging Networks with Global Peak Constraints,” IEEE Transactions on Sustainable Computing, 2020. doi:10.1109/TSUSC.2020.2979854

[BibTeX] [Abstract] [Download PDF]Electricity bill constitutes a significant portion of operational costs for large scale data centers. Empowering data centers with on-site storages can reduce the electricity bill by shaping the energy procurement from deregulated electricity markets with real-time price fluctuations. This paper focuses on designing energy procurement and storage management strategies to minimize the electricity bill of storage-assisted data centers. Designing such strategies is challenging since the net energy demand of the data center and electricity market prices are not known in advance, and the underlying problem is coupled over time due to evolution of the storage level. Using competitive ratio as the performance measure, we propose an online algorithm that determines the energy procurement and storage management strategies using a threshold based policy. Our algorithm achieves the optimal competitive ratio of as a function of the price fluctuation ratio. We validate the algorithm using data traces from electricity markets and data-center energy demands. The results show that our algorithm achieves close to the offline optimal performance and outperforms existing alternatives.

`@article{bhlcm2019tsusc, abstract = {Electricity bill constitutes a significant portion of operational costs for large scale data centers. Empowering data centers with on-site storages can reduce the electricity bill by shaping the energy procurement from deregulated electricity markets with real-time price fluctuations. This paper focuses on designing energy procurement and storage management strategies to minimize the electricity bill of storage-assisted data centers. Designing such strategies is challenging since the net energy demand of the data center and electricity market prices are not known in advance, and the underlying problem is coupled over time due to evolution of the storage level. Using competitive ratio as the performance measure, we propose an online algorithm that determines the energy procurement and storage management strategies using a threshold based policy. Our algorithm achieves the optimal competitive ratio of as a function of the price fluctuation ratio. We validate the algorithm using data traces from electricity markets and data-center energy demands. The results show that our algorithm achieves close to the offline optimal performance and outperforms existing alternatives.}, author = {Bahram, Alina and Hajiesmaili, Mohammad H. and Lee, Zachary and Crespi, Noel and Mallada, Enrique}, doi = {10.1109/TSUSC.2020.2979854}, grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979,EPCN-1711188,}, journal = {IEEE Transactions on Sustainable Computing}, month = {1}, title = {Online EV Scheduling Algorithms for Adaptive Charging Networks with Global Peak Constraints}, url = {https://mallada.ece.jhu.edu/pubs/2020-TSUSC-BHLCM.pdf}, year = {2020} }`

- L. Yang, M. H. Hajiesmaili, R. Sitaraman, A. Wierman, E. Mallada, and W. S. Wong, “Online Linear Optimization with Inventory Management Constraints,” Proceedings of ACM on Measurement and Analysis of Computing Systems (POMACS), vol. 3, iss. 2, 2020. doi:10.1145/3379482

[BibTeX] [Abstract] [Download PDF]This paper considers the problem of online linear optimization with inventory management constraints. Specifically, we consider an online scenario where a decision-maker needs to satisfy her time-varying demand for some units of an asset, either from a market with a time-varying price or from her own inventory. In each time slot, the decision-maker is presented a (linear) price and must immediately decide the amount to purchase to cover the demand and/or to store in inventory for future use. The inventory has a limited capacity and can be used to buy and store assets at a low price and in order to cover the demand when the price is high. The ultimate goal of the decision-maker is to cover the demand at each time slot while minimizing the cost of buying assets from the market. We propose ARP, an online algorithm for linear programming with inventory constraints, and ARPRate, an extended version that handles rate constraints to/from the inventory. Both ARP and ARPRate achieve optimal competitive ratios, meaning that no other online algorithm can achieve a better theoretical guarantee. To illustrate the results, we use the proposed algorithms in a case study focused on energy procurement and storage management strategies for data centers.

`@article{yhswmw2020pomacs, abstract = {This paper considers the problem of online linear optimization with inventory management constraints. Specifically, we consider an online scenario where a decision-maker needs to satisfy her time-varying demand for some units of an asset, either from a market with a time-varying price or from her own inventory. In each time slot, the decision-maker is presented a (linear) price and must immediately decide the amount to purchase to cover the demand and/or to store in inventory for future use. The inventory has a limited capacity and can be used to buy and store assets at a low price and in order to cover the demand when the price is high. The ultimate goal of the decision-maker is to cover the demand at each time slot while minimizing the cost of buying assets from the market. We propose ARP, an online algorithm for linear programming with inventory constraints, and ARPRate, an extended version that handles rate constraints to/from the inventory. Both ARP and ARPRate achieve optimal competitive ratios, meaning that no other online algorithm can achieve a better theoretical guarantee. To illustrate the results, we use the proposed algorithms in a case study focused on energy procurement and storage management strategies for data centers.}, address = {New York, NY, USA}, author = {Yang, Lin and Hajiesmaili, Mohammad H. and Sitaraman, Ramesh and Wierman, Adam and Mallada, Enrique and Wong, Wing S.}, date = {2020}, doi = {10.1145/3379482}, grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448,EPCN-1711188}, journal = {Proceedings of ACM on Measurement and Analysis of Computing Systems (POMACS)}, month = {6}, note = {also in ACM Sigmetrics 2020}, number = {2}, publisher = {ACM}, title = {Online Linear Optimization with Inventory Management Constraints}, url = {https://mallada.ece.jhu.edu/pubs/2020-POMACS-YHSWMW.pdf}, volume = {3}, year = {2020} }`

- F. Paganini and E. Mallada, “Global analysis of synchronization performance for power systems: bridging the theory-practice gap,” IEEE Transactions on Automatic Control, vol. 67, iss. 7, pp. 3007-3022, 2020. doi:10.1109/TAC.2019.2942536

[BibTeX] [Abstract] [Download PDF]The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance, and analyzed under highly simplified assumptions. In this paper we extend this approach to more realistic network scenarios, and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a system-wide frequency that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define –and compute in closed form– several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the system frequency, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a synchronization cost that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.

`@article{pm2020tac, abstract = {The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance, and analyzed under highly simplified assumptions. In this paper we extend this approach to more realistic network scenarios, and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a system-wide frequency that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define --and compute in closed form-- several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the system frequency, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a synchronization cost that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.}, author = {Paganini, Fernando and Mallada, Enrique}, doi = {10.1109/TAC.2019.2942536}, grants = {CPS-1544771, AMPS-1736448, EPCN-1711188, CAREER-1752362, ENERGISE-DE-EE0008006}, journal = {IEEE Transactions on Automatic Control}, month = {7}, number = {7}, pages = {3007-3022}, title = {Global analysis of synchronization performance for power systems: bridging the theory-practice gap}, url = {https://mallada.ece.jhu.edu/pubs/2020-TAC-PM.pdf}, volume = {67}, year = {2020} }`

- E. Weitenberg, Y. Jiang, C. Zhao, E. Mallada, C. De Persis, and F. Dorfler, “Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs,” IEEE Transactions on Automatic Control, vol. 64, iss. 10, pp. 3967-3982, 2019. doi:10.1109/TAC.2018.2884650

[BibTeX] [Abstract] [Download PDF]Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers. In this paper we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.

`@article{wjzmdd2019tac, abstract = {Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers. In this paper we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.}, author = {Weitenberg, Erik and Jiang, Yan and Zhao, Changhong and Mallada, Enrique and De Persis, Claudio and Dorfler, Florian}, doi = {10.1109/TAC.2018.2884650}, grants = {CPS-1544771, EPCN-1711188, AMPS-1736448, CAREER-1752362, ENERGISE-DE-EE0008006}, issn = {0018-9286}, journal = {IEEE Transactions on Automatic Control}, keywords = {Power Networks}, month = {10}, number = {10}, pages = {3967-3982}, title = {Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs}, url = {https://mallada.ece.jhu.edu/pubs/2019-TAC-WJZMDD.pdf}, volume = {64}, year = {2019} }`

- R. Pates and E. Mallada, “Robust Scale Free Synthesis for Frequency Regulation in Power Systems,” IEEE Transactions on Control of Network Systems, vol. 6, iss. 3, pp. 1174-1184, 2019. doi:10.1109/TCNS.2019.2922503

[BibTeX] [Abstract] [Download PDF]This paper develops a framework for power system stability analysis, that allows for the decentralised design of frequency controllers. The method builds on a novel decentralised stability criterion, expressed as a positive real requirement, that depends only on the dynamics of the components at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The criterion is both robust to network uncertainties as well as heterogeneous network components, and it can be verified using several standard frequency response, state space, and circuit theory analysis tools. Moreover, it allows to formulate a scale free synthesis problem, that depends on individual bus dynamics and leverages tools from Hinf optimal control. Notably, unlike similar passivity methods, our framework certifies the stability of several existing (non-passive) power system control schemes and allows to study robustness with respect to delays.

`@article{pm2019tcns, abstract = {This paper develops a framework for power system stability analysis, that allows for the decentralised design of frequency controllers. The method builds on a novel decentralised stability criterion, expressed as a positive real requirement, that depends only on the dynamics of the components at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The criterion is both robust to network uncertainties as well as heterogeneous network components, and it can be verified using several standard frequency response, state space, and circuit theory analysis tools. Moreover, it allows to formulate a scale free synthesis problem, that depends on individual bus dynamics and leverages tools from Hinf optimal control. Notably, unlike similar passivity methods, our framework certifies the stability of several existing (non-passive) power system control schemes and allows to study robustness with respect to delays.}, author = {Pates, Richard and Mallada, Enrique}, doi = {10.1109/TCNS.2019.2922503}, grants = {CPS:1544771, EPCN-1711188, AMPS-1736448, CAREER-1752362}, journal = {IEEE Transactions on Control of Network Systems}, keywords = {Network Control; Power Networks}, month = {9}, number = {3}, pages = {1174-1184}, title = {Robust Scale Free Synthesis for Frequency Regulation in Power Systems}, url = {https://mallada.ece.jhu.edu/pubs/2019-TCNS-PM.pdf}, volume = {6}, year = {2019} }`

- C. Zhao, E. Mallada, S. H. Low, and J. W. Bialek, “Distributed plug-and-play optimal generator and load control for power system frequency regulation,” International Journal of Electric Power and Energy Systems, vol. 101, pp. 1-12, 2018. doi:https://doi.org/10.1016/j.ijepes.2018.03.014

[BibTeX] [Abstract] [Download PDF]A distributed control scheme, which can be implemented on generators and controllable loads in a plug-and-play manner, is proposed for power system frequency regulation. The proposed scheme is based on local measurements, local computation, and neighborhood information exchanges over a communication network with an arbitrary (but connected) topology. In the event of a sudden change in generation or load, the proposed scheme can restore the nominal frequency and the reference inter-area power flows, while minimizing the total cost of control for participating generators and loads. Power network stability under the proposed control is proved with a relatively realistic model which includes nonlinear power flow and a generic (potentially nonlinear or high-order) turbine-governor model, and further with first- and second-order turbine-governor models as special cases. In simulations, the proposed control scheme shows a comparable performance to the existing automatic generation control (AGC) when implemented only on the generator side, and demonstrates better dynamic characteristics that AGC when each scheme is implemented on both generators and controllable loads.

`@article{zmlb2018ijepes, abstract = {A distributed control scheme, which can be implemented on generators and controllable loads in a plug-and-play manner, is proposed for power system frequency regulation. The proposed scheme is based on local measurements, local computation, and neighborhood information exchanges over a communication network with an arbitrary (but connected) topology. In the event of a sudden change in generation or load, the proposed scheme can restore the nominal frequency and the reference inter-area power flows, while minimizing the total cost of control for participating generators and loads. Power network stability under the proposed control is proved with a relatively realistic model which includes nonlinear power flow and a generic (potentially nonlinear or high-order) turbine-governor model, and further with first- and second-order turbine-governor models as special cases. In simulations, the proposed control scheme shows a comparable performance to the existing automatic generation control (AGC) when implemented only on the generator side, and demonstrates better dynamic characteristics that AGC when each scheme is implemented on both generators and controllable loads.}, author = {Zhao, Changhong and Mallada, Enrique and Low, Steven H and Bialek, Janusz W}, doi = {https://doi.org/10.1016/j.ijepes.2018.03.014}, grants = {W911NF-17-1-0092, 1544771, 1711188, 1736448, 1752362}, issn = {0142-0615}, journal = {International Journal of Electric Power and Energy Systems}, keywords = {Power Networks; Frequency Control}, month = {10}, pages = {1 -12}, title = {Distributed plug-and-play optimal generator and load control for power system frequency regulation}, url = {https://mallada.ece.jhu.edu/pubs/2018-IJEPES-ZMLB.pdf}, volume = {101}, year = {2018} }`

- A. Cherukuri, E. Mallada, S. H. Low, and J. Cortes, “The role of convexity on saddle-point dynamics: Lyapunov function and robustness,” IEEE Transactions on Automatic Control, vol. 63, iss. 8, pp. 2449-2464, 2018. doi:10.1109/TAC.2017.2778689

[BibTeX] [Abstract] [Download PDF]This paper studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We examine the role that the local and/or global nature of the convexity-concavity properties of the saddle function plays in guaranteeing convergence and robustness of the dynamics. Under the assumption that the saddle function is twice continuously differentiable, we provide a novel characterization of the omega-limit set of the trajectories of this dynamics in terms of the diagonal blocks of the Hessian. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexity-concavity of the saddle function. When strong convexity-concavity holds globally, we establish three results. First, we identify a Lyapunov function (that decreases strictly along the trajectory) for the projected saddle-point dynamics when the saddle function corresponds to the Lagrangian of a general constrained convex optimization problem. Second, for the particular case when the saddle function is the Lagrangian of an equality-constrained optimization problem, we show input-to-state stability of the saddle-point dynamics by providing an ISS Lyapunov function. Third, we use the latter result to design an opportunistic state-triggered implementation of the dynamics. Various examples illustrate our results.

`@article{cmlc2018tac, abstract = {This paper studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We examine the role that the local and/or global nature of the convexity-concavity properties of the saddle function plays in guaranteeing convergence and robustness of the dynamics. Under the assumption that the saddle function is twice continuously differentiable, we provide a novel characterization of the omega-limit set of the trajectories of this dynamics in terms of the diagonal blocks of the Hessian. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexity-concavity of the saddle function. When strong convexity-concavity holds globally, we establish three results. First, we identify a Lyapunov function (that decreases strictly along the trajectory) for the projected saddle-point dynamics when the saddle function corresponds to the Lagrangian of a general constrained convex optimization problem. Second, for the particular case when the saddle function is the Lagrangian of an equality-constrained optimization problem, we show input-to-state stability of the saddle-point dynamics by providing an ISS Lyapunov function. Third, we use the latter result to design an opportunistic state-triggered implementation of the dynamics. Various examples illustrate our results.}, author = {Cherukuri, Ashish and Mallada, Enrique and Steven H. Low and Jorge Cortes}, doi = {10.1109/TAC.2017.2778689}, grants = {W911NF-17-1-0092}, journal = {IEEE Transactions on Automatic Control}, keywords = {Saddle-Point Dynamics; Caratheodory solutions}, month = {08}, number = {8}, pages = {2449-2464}, title = {The role of convexity on saddle-point dynamics: Lyapunov function and robustness}, url = {https://mallada.ece.jhu.edu/pubs/2018-TAC-CMLC.pdf}, volume = {63}, year = {2018} }`

- E. Mallada, C. Zhao, and S. H. Low, “Optimal load-side control for frequency regulation in smart grids,” IEEE Transactions on Automatic Control, vol. 62, iss. 12, pp. 6294-6309, 2017. doi:10.1109/TAC.2017.2713529

[BibTeX] [Abstract] [Download PDF]Frequency control rebalances supply and demand while maintaining the network state within operational margins. It is implemented using fast ramping reserves that are expensive and wasteful, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints. In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. Our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike generation-side), can allocate load updates optimally, and can maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and robust to unknown load parameters. Simulations are used to illustrate the properties of our solution.

`@article{mzl2017tac, abstract = {Frequency control rebalances supply and demand while maintaining the network state within operational margins. It is implemented using fast ramping reserves that are expensive and wasteful, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints. In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. Our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike generation-side), can allocate load updates optimally, and can maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and robust to unknown load parameters. Simulations are used to illustrate the properties of our solution.}, author = {Mallada, Enrique and Zhao, Changhong and Low, Steven H}, doi = {10.1109/TAC.2017.2713529}, grants = {1544771}, journal = {IEEE Transactions on Automatic Control}, keywords = {Power Networks}, month = {12}, number = {12}, pages = {6294-6309}, title = {Optimal load-side control for frequency regulation in smart grids}, url = {https://mallada.ece.jhu.edu/pubs/2017-TAC-MZL.pdf}, volume = {62}, year = {2017} }`

- D. Cai, E. Mallada, and A. Wierman, “Distributed optimization decomposition for joint economic dispatch and frequency regulation,” IEEE Transactions on Power Systems, vol. 32, iss. 6, pp. 4370-4385, 2017. doi:10.1109/TPWRS.2017.2682235

[BibTeX] [Abstract] [Download PDF]Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

`@article{cmw2017tps, abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.}, author = {Cai, Desmond and Mallada, Enrique and Wierman, Adam}, doi = {10.1109/TPWRS.2017.2682235}, grants = {1544771}, journal = {IEEE Transactions on Power Systems}, keywords = {Power Networks; Markets}, month = {11}, number = {6}, pages = {4370-4385}, title = {Distributed optimization decomposition for joint economic dispatch and frequency regulation}, url = {https://mallada.ece.jhu.edu/pubs/2017-TPS-CMW.pdf}, volume = {32}, year = {2017} }`

- K. Dvijotham, E. Mallada, and J. W. Simpson-Porco, “High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms,” IEEE Control Systems Letters, vol. 1, iss. 2, pp. 322-327, 2017. doi:10.1109/LCSYS.2017.2717578

[BibTeX] [Abstract] [Download PDF]The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such solutions exist, or when these algorithms can be guaranteed to converge. In this paper, we derive necessary and sufficient conditions for the existence and uniqueness of a power flow solution in balanced radial distribution networks with homogeneous (uniform R/X ratio) transmission lines. We study three distinct solution methods: fixed point iterations, convex relaxations, and energy functions – we show that the three algorithms successfully find a solution if and only if a solution exists. Moreover, all three algorithms always find the unique high-voltage solution to the power flow equations, the existence of which we formally establish. At this solution, we prove that (i) voltage magnitudes are increasing functions of the reactive power injections, (ii) the solution is a continuous function of the injections, and (iii) the solution is the last one to vanish as the system is loaded past the feasibility boundary.

`@article{dms2017ieee-csl, abstract = {The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such solutions exist, or when these algorithms can be guaranteed to converge. In this paper, we derive necessary and sufficient conditions for the existence and uniqueness of a power flow solution in balanced radial distribution networks with homogeneous (uniform R/X ratio) transmission lines. We study three distinct solution methods: fixed point iterations, convex relaxations, and energy functions - we show that the three algorithms successfully find a solution if and only if a solution exists. Moreover, all three algorithms always find the unique high-voltage solution to the power flow equations, the existence of which we formally establish. At this solution, we prove that (i) voltage magnitudes are increasing functions of the reactive power injections, (ii) the solution is a continuous function of the injections, and (iii) the solution is the last one to vanish as the system is loaded past the feasibility boundary.}, author = {Dvijotham, Krishnamurthy and Mallada, Enrique and Simpson-Porco, John W.}, doi = {10.1109/LCSYS.2017.2717578}, grants = {1544771}, journal = {IEEE Control Systems Letters}, keywords = {Power Networks; Power Flow Solutions}, month = {10}, number = {2}, pages = {322-327}, title = {High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms}, url = {https://mallada.ece.jhu.edu/pubs/2017-IEEE-CSL-DMS.pdf}, volume = {1}, year = {2017} }`

- A. Gushchin, E. Mallada, and A. Tang, “Phase-coupled oscillators with plastic coupling: Synchronization and stability,” IEEE Transactions on Network Science and Engineering, vol. 3, iss. 4, pp. 240-256, 2016. doi:10.1109/TNSE.2016.2605096

[BibTeX] [Abstract] [Download PDF]In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that, under mild assumptions, such systems are gradient systems, and always achieve frequency synchronization. Furthermore, we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion (necessary and sufficient condition) of stability of equilibria. For both, tree and arbitrary topologies, we provide sufficient conditions for phase-locking, i.e. convergence to a stable equilibrium almost surely. We additionally find conditions when the system possesses a unique stable equilibrium, and thus, almost global stability follows. Several examples are used to demonstrate variety of equilibria the system has, their dependence on system’s parameters, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.

`@article{gmt2016tnse, abstract = {In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that, under mild assumptions, such systems are gradient systems, and always achieve frequency synchronization. Furthermore, we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion (necessary and sufficient condition) of stability of equilibria. For both, tree and arbitrary topologies, we provide sufficient conditions for phase-locking, i.e. convergence to a stable equilibrium almost surely. We additionally find conditions when the system possesses a unique stable equilibrium, and thus, almost global stability follows. Several examples are used to demonstrate variety of equilibria the system has, their dependence on system's parameters, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.}, author = {Gushchin, Andrey and Mallada, Enrique and Tang, Ao}, doi = {10.1109/TNSE.2016.2605096}, journal = {IEEE Transactions on Network Science and Engineering}, keywords = {Synchronization}, month = {09}, number = {4}, pages = {240-256}, title = {Phase-coupled oscillators with plastic coupling: Synchronization and stability}, url = {https://mallada.ece.jhu.edu/pubs/2016-TNSE-GMT.pdf}, volume = {3}, year = {2016} }`

- A. Cherukuri, E. Mallada, and J. Cortes, “Asymptotic convergence of constrained primal–dual dynamics,” Systems & Control Letters, vol. 87, pp. 10-15, 2016. doi:10.1016/j.sysconle.2015.10.006

[BibTeX] [Abstract] [Download PDF]This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer.

`@article{cmc2016scl, abstract = {This paper studies the asymptotic convergence properties of the primal--dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal--dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal--dual optimizers are globally asymptotically stable under the primal--dual dynamics and that each solution of the dynamics converges to an optimizer. }, author = {Ashish Cherukuri and Mallada, Enrique and Jorge Cortes}, doi = {10.1016/j.sysconle.2015.10.006}, issn = {0167-6911}, journal = {Systems & Control Letters}, keywords = {Caratheodory solutions; Optimization; Saddle-Point Dynamics}, month = {01}, pages = {10 - 15}, title = {Asymptotic convergence of constrained primal--dual dynamics}, url = {https://mallada.ece.jhu.edu/pubs/2016-SCL-CMC.pdf}, volume = {87}, web = {http://www.sciencedirect.com/science/article/pii/S0167691115002078}, year = {2016} }`

- E. Mallada, R. A. Freeman, and A. Tang, “Distributed synchronization of heterogeneous oscillators on networks with arbitrary topology,” IEEE Transactions on Control of Network Systems, vol. 3, iss. 1, pp. 12-23, 2016. doi:10.1109/TCNS.2015.2428371

[BibTeX] [Abstract] [Download PDF]Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted messages. In this paper, we study the problem of using distributed control to achieve both phase and frequency synchronization of a network of coupled heterogeneous nonlinear oscillators. Not only do our controllers guarantee zero phase error in steady state under arbitrary frequency heterogeneity, but they also require little knowledge of the oscillator nonlinearities and network topology. Furthermore, we provide a global convergence analysis, in the absence of noise and propagation delay, for the resulting nonlinear system whose phase vector evolves on the n-torus.

`@article{mft2016tcns, abstract = {Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted messages. In this paper, we study the problem of using distributed control to achieve both phase and frequency synchronization of a network of coupled heterogeneous nonlinear oscillators. Not only do our controllers guarantee zero phase error in steady state under arbitrary frequency heterogeneity, but they also require little knowledge of the oscillator nonlinearities and network topology. Furthermore, we provide a global convergence analysis, in the absence of noise and propagation delay, for the resulting nonlinear system whose phase vector evolves on the n-torus.}, author = {Mallada, Enrique and Freeman, Randy A and Tang, Ao}, doi = {10.1109/TCNS.2015.2428371}, journal = {IEEE Transactions on Control of Network Systems}, keywords = {Coupled Oscillators; Synchronization}, month = {3}, number = {1}, pages = {12-23}, title = {Distributed synchronization of heterogeneous oscillators on networks with arbitrary topology}, url = {https://mallada.ece.jhu.edu/pubs/2016-TCNS-MFT.pdf}, volume = {3}, year = {2016} }`

- E. Mallada, X. Meng, M. Hack, L. Zhang, and A. Tang, “Skewless network clock synchronization without discontinuity: Convergence and performance,” IEEE/ACM Transactions on Networking (TON), vol. 23, iss. 5, pp. 1619-1633, 2015. doi:10.1109/TNET.2014.2345692

[BibTeX] [Abstract] [Download PDF]This paper examines synchronization of computer clocks connected via a data network and proposes a skewless algorithm to synchronize them. Unlike existing solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, our solution achieves synchronization without these problems. We first analyze the convergence property of the algorithm and provide explicit necessary and sufficient conditions on the parameters to guarantee synchronization. We then study the effect of noisy measurements (jitter) and frequency drift (wander) on the offsets and synchronization frequency, and further optimize the parameter values to minimize their variance. Our study reveals a few insights, for example, we show that our algorithm can converge even in the presence of timing loops and noise, provided that there is a well-defined leader. This marks a clear contrast with current standards such as NTP and PTP, where timing loops are specifically avoided. Furthermore, timing loops can even be beneficial in our scheme as it is demonstrated that highly connected subnetworks can collectively outperform individual clients when the time source has large jitter. The results are supported by experiments running on a cluster of IBM BladeCenter servers with Linux.

`@article{mmhzt2015ton, abstract = {This paper examines synchronization of computer clocks connected via a data network and proposes a skewless algorithm to synchronize them. Unlike existing solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, our solution achieves synchronization without these problems. We first analyze the convergence property of the algorithm and provide explicit necessary and sufficient conditions on the parameters to guarantee synchronization. We then study the effect of noisy measurements (jitter) and frequency drift (wander) on the offsets and synchronization frequency, and further optimize the parameter values to minimize their variance. Our study reveals a few insights, for example, we show that our algorithm can converge even in the presence of timing loops and noise, provided that there is a well-defined leader. This marks a clear contrast with current standards such as NTP and PTP, where timing loops are specifically avoided. Furthermore, timing loops can even be beneficial in our scheme as it is demonstrated that highly connected subnetworks can collectively outperform individual clients when the time source has large jitter. The results are supported by experiments running on a cluster of IBM BladeCenter servers with Linux.}, author = {Mallada, Enrique and Meng, Xiaoqiao and Hack, Michel and Zhang, Li and Tang, Ao}, doi = {10.1109/TNET.2014.2345692}, issn = {1063-6692}, journal = {IEEE/ACM Transactions on Networking (TON)}, keywords = {Synchronization; Networking}, month = {10}, number = {5}, pages = {1619--1633}, rating = {1}, title = {Skewless network clock synchronization without discontinuity: Convergence and performance}, url = {https://mallada.ece.jhu.edu/pubs/2015-ToN-MMHZT.pdf}, volume = {23}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6883234}, year = {2015} }`

- M. Wang, W. Xu, E. Mallada, and A. Tang, “Sparse recovery with graph constraints,” IEEE Transactions on Information Theory, vol. 61, iss. 2, pp. 1028-1044, 2015. doi:10.1109/TIT.2014.2376955

[BibTeX] [Abstract] [Download PDF]Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor the key characteristics of large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse signals in the presence of network topological constraints. Unlike conventional sparse recovery where a measurement can contain any subset of the unknown variables, we use a graph to characterize the topological constraints and allow an additive measurement over nodes (unknown variables) only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs, and the number of measurements by our construction is less than that needed by existing random constructions. Moreover, our construction for a line network is provably optimal in the sense that it requires the minimum number of measurements. A measurement construction algorithm for general graphs is also proposed and evaluated. For any given graph G with n nodes, we derive bounds of the minimum number of measurements needed to recover any k-sparse vector over G (Mk,nG). Using the Erdös-Rényi random graph as an example, we characterize the dependence of Mk,nG on the graph structure. This paper suggests that Mk,nG may serve as a graph connectivity metric.

`@article{wxmt2015tit, abstract = {Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor the key characteristics of large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse signals in the presence of network topological constraints. Unlike conventional sparse recovery where a measurement can contain any subset of the unknown variables, we use a graph to characterize the topological constraints and allow an additive measurement over nodes (unknown variables) only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs, and the number of measurements by our construction is less than that needed by existing random constructions. Moreover, our construction for a line network is provably optimal in the sense that it requires the minimum number of measurements. A measurement construction algorithm for general graphs is also proposed and evaluated. For any given graph G with n nodes, we derive bounds of the minimum number of measurements needed to recover any k-sparse vector over G (Mk,nG). Using the Erdös-Rényi random graph as an example, we characterize the dependence of Mk,nG on the graph structure. This paper suggests that Mk,nG may serve as a graph connectivity metric.}, author = {Wang, M. and Xu, W. and Mallada, Enrique and Tang, A.}, doi = {10.1109/TIT.2014.2376955}, journal = {IEEE Transactions on Information Theory}, keywords = {Sparse Recovery}, month = {02}, number = {2}, pages = {1028-1044}, title = {Sparse recovery with graph constraints}, url = {https://mallada.ece.jhu.edu/pubs/2015-TIT-WXMT.pdf}, volume = {61}, year = {2015} }`

- E. Mallada and A. Tang, “Synchronization of weakly coupled oscillators: coupling, delay and topology,” Journal of Physics A: Mathematical and Theoretical, vol. 46, iss. 50, p. 505101, 2013. doi:10.1088/1751-8113/46/50/505101

[BibTeX] [Abstract] [Download PDF]There are three key factors in a system of coupled oscillators that characterize the interaction between them: coupling (how to affect), delay (when to affect) and topology (whom to affect). The existing work on each of these factors has mainly focused on special cases. With new angles and tools, this paper makes progress in relaxing some assumptions on these factors. There are three main results in this paper. Firstly, by using results from algebraic graph theory, a sufficient condition is obtained that can be used to check equilibrium stability. This condition works for arbitrary topology, generalizing existing results and also leading to a sufficient condition on the coupling function which guarantees that the system will reach synchronization. Secondly, it is known that identical oscillators with sin () coupling functions are guaranteed to synchronize in phase on a complete graph. Our results prove that in many cases certain structures such as symmetry and concavity, rather than the exact shape of the coupling function, are the keys for global synchronization. Finally, the effect of heterogenous delays is investigated. Using mean field theory, a system of delayed coupled oscillators is approximated by a non-delayed one whose coupling depends on the delay distribution. This shows how the stability properties of the system depend on the delay distribution and allows us to predict its behavior. In particular, we show that for sin () coupling, heterogeneous delays are equivalent to homogeneous delays. Furthermore, we can use our novel sufficient instability condition to show that heterogeneity, i.e. wider delay distribution, can help reach in-phase synchronization.

`@article{mt2013jopa, abstract = {There are three key factors in a system of coupled oscillators that characterize the interaction between them: coupling (how to affect), delay (when to affect) and topology (whom to affect). The existing work on each of these factors has mainly focused on special cases. With new angles and tools, this paper makes progress in relaxing some assumptions on these factors. There are three main results in this paper. Firstly, by using results from algebraic graph theory, a sufficient condition is obtained that can be used to check equilibrium stability. This condition works for arbitrary topology, generalizing existing results and also leading to a sufficient condition on the coupling function which guarantees that the system will reach synchronization. Secondly, it is known that identical oscillators with sin () coupling functions are guaranteed to synchronize in phase on a complete graph. Our results prove that in many cases certain structures such as symmetry and concavity, rather than the exact shape of the coupling function, are the keys for global synchronization. Finally, the effect of heterogenous delays is investigated. Using mean field theory, a system of delayed coupled oscillators is approximated by a non-delayed one whose coupling depends on the delay distribution. This shows how the stability properties of the system depend on the delay distribution and allows us to predict its behavior. In particular, we show that for sin () coupling, heterogeneous delays are equivalent to homogeneous delays. Furthermore, we can use our novel sufficient instability condition to show that heterogeneity, i.e. wider delay distribution, can help reach in-phase synchronization.}, author = {Mallada, Enrique and Tang, Ao}, doi = {10.1088/1751-8113/46/50/505101}, journal = {Journal of Physics A: Mathematical and Theoretical}, keywords = {Coupled Oscillators; Synchronization}, month = {12}, number = {50}, pages = {505101}, title = {Synchronization of weakly coupled oscillators: coupling, delay and topology}, url = {https://mallada.ece.jhu.edu/pubs/2013-JOPA-MT.pdf}, volume = {46}, year = {2013} }`

- F. Paganini and E. Mallada, “A unified approach to congestion control and node-based multipath routing,” IEEE/ACM Transactions on Networking (TON), vol. 17, iss. 5, pp. 1413-1426, 2009. doi:10.1109/TNET.2008.2011902

[BibTeX] [Abstract] [Download PDF]The paper considers a TCP/IP-style network with flow control at end-systems based on congestion feedback and routing decisions at network nodes on a per-destination basis. The main generalization with respect to standard IP is to allow routers to split their traffic in a controlled way between the outgoing links. We formulate global optimization criteria, combining those used in the congestion control and traffic engineering, and propose decentralized controllers at sources and routers to reach these optimal points, based on congestion price feedback. We first consider adapting the traffic splits at routers to follow the negative price gradient; we prove this is globally stabilizing when combined with primal congestion control, but can exhibit oscillations in the case of dual congestion control. We then propose an alternative anticipatory control of routing, proving its stability for the case of dual congestion control. We present a concrete implementation of such algorithms, based on queueing delay as congestion price. We use TCP-FAST for congestion control and develop a multipath variant of the distance vector routing protocol RIP. We demonstrate through ns2-simulations the collective behavior of the system, in particular that it reaches the desired equilibrium points.

`@article{pm2009ton, abstract = {The paper considers a TCP/IP-style network with flow control at end-systems based on congestion feedback and routing decisions at network nodes on a per-destination basis. The main generalization with respect to standard IP is to allow routers to split their traffic in a controlled way between the outgoing links. We formulate global optimization criteria, combining those used in the congestion control and traffic engineering, and propose decentralized controllers at sources and routers to reach these optimal points, based on congestion price feedback. We first consider adapting the traffic splits at routers to follow the negative price gradient; we prove this is globally stabilizing when combined with primal congestion control, but can exhibit oscillations in the case of dual congestion control. We then propose an alternative anticipatory control of routing, proving its stability for the case of dual congestion control. We present a concrete implementation of such algorithms, based on queueing delay as congestion price. We use TCP-FAST for congestion control and develop a multipath variant of the distance vector routing protocol RIP. We demonstrate through ns2-simulations the collective behavior of the system, in particular that it reaches the desired equilibrium points.}, author = {Paganini, Fernando and Mallada, Enrique}, doi = {10.1109/TNET.2008.2011902}, journal = {IEEE/ACM Transactions on Networking (TON)}, keywords = {Networking}, month = {10}, number = {5}, pages = {1413--1426}, publisher = {IEEE}, title = {A unified approach to congestion control and node-based multipath routing}, url = {https://mallada.ece.jhu.edu/pubs/2009-ToN-MP.pdf}, volume = {17}, web = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5200323}, year = {2009} }`

**Conference Proceedings**

- H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” in American Control Conference, 2021, pp. 1-6.

[BibTeX] [Abstract] [Download PDF]We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models –based on frequency weighted balanced truncation– that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.

`@inproceedings{mpm2021acc, abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.}, author = {Min, Hancheng and Paganini, Fernando and Mallada, Enrique}, booktitle = {American Control Conference}, grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092}, month = {1}, pages = {1-6}, pubstate = {accepted}, record = {submitted Sep. 2020}, title = {Accurate Reduced Order Models for Coherent Heterogeneous Generators}, url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-MPM.pdf}, year = {2021} }`

- J. Guthrie and E. Mallada, “Outer Approximations of Minkowski Operations on Complex Sets via Sum-of-Squares Optimization,” in American Control Conference, 2021, pp. 1-7.

[BibTeX] [Abstract] [Download PDF]We study the problem of finding closed-form outerapproximations of Minkowski sums and products of sets inthe complex plane. Using polar coordinates, we pose this asan optimization problem in which we find a pair of contoursthat give lower and upper bounds on the radial distance ata given angle. Through a series of variable transformationswe rewrite this as a sum-of-squares optimization problem.Numerical examples are given to demonstrate the performance.

`@inproceedings{gm2021acc, abstract = {We study the problem of finding closed-form outerapproximations of Minkowski sums and products of sets inthe complex plane. Using polar coordinates, we pose this asan optimization problem in which we find a pair of contoursthat give lower and upper bounds on the radial distance ata given angle. Through a series of variable transformationswe rewrite this as a sum-of-squares optimization problem.Numerical examples are given to demonstrate the performance.}, author = {Guthrie, James and Mallada, Enrique}, booktitle = {American Control Conference}, grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979}, month = {1}, pages = {1-7}, pubstate = {accepted}, record = {submitted Sep. 2020}, title = {Outer Approximations of Minkowski Operations on Complex Sets via Sum-of-Squares Optimization}, url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-GM.pdf}, year = {2021} }`

- R. K. Bansal, P. You, D. F. Gayme, and E. Mallada, “Storage Degradation Aware Economic Dispatch,” in American Control Conference, 2021, pp. 1-6.

[BibTeX] [Abstract] [Download PDF]In this paper, we formulate a cycling cost aware economic dispatch problem that co-optimizes generation and storage dispatch while taking into account cycle based storage degradation cost. Our approach exploits the Rainflow cycle counting algorithm to quantify storage degradation for each charging and discharging half-cycle based on its depth. We show that the dispatch is optimal for individual participants in the sense that it maximizes the profit of generators and storage units, under price taking assumptions. We further provide a condition under which the optimal storage response is unique for given market clearing prices. Simulations using data from the New York Independent System Operator (NYISO) illustrate the optimization framework. In particular, they show that the generation-centric dispatch that does not account for storage degradation is insufficient to guarantee storage profitability.

`@inproceedings{bygm2021acc, abstract = {In this paper, we formulate a cycling cost aware economic dispatch problem that co-optimizes generation and storage dispatch while taking into account cycle based storage degradation cost. Our approach exploits the Rainflow cycle counting algorithm to quantify storage degradation for each charging and discharging half-cycle based on its depth. We show that the dispatch is optimal for individual participants in the sense that it maximizes the profit of generators and storage units, under price taking assumptions. We further provide a condition under which the optimal storage response is unique for given market clearing prices. Simulations using data from the New York Independent System Operator (NYISO) illustrate the optimization framework. In particular, they show that the generation-centric dispatch that does not account for storage degradation is insufficient to guarantee storage profitability. }, author = {Bansal, Rajni Kant and You, Pengcheng and Gayme, Dennice F. and Mallada, Enrique}, booktitle = {American Control Conference}, grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979}, month = {1}, pages = {1-6}, pubstate = {accepted}, record = {submitted Sep. 2020}, title = {Storage Degradation Aware Economic Dispatch}, url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-BYGM.pdf}, year = {2021} }`

- H. Min, S. Tarmoun, R. Vidal, and E. Mallada, “On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks,” in International Conference of Machine Learning (ICML), 2021, pp. 1-9.

[BibTeX] [Abstract] [Download PDF]Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon is to study how initialization and overparametrization affect convergence and implicit bias of training algorithms. In this paper, we present a novel analysis of single-hidden-layer linear networks trained under gradient flow, which connects initialization, optimization, and overparametrization. Firstly, we show that the squared loss converges exponentially to its optimum at a rate that depends on the level of imbalance of the initialization. Secondly, we show that proper initialization constrains the dynamics of the network parameters to lie within an invariant set. In turn, minimizing the loss over this set leads to the min-norm solution. Finally, we show that large hidden layer width, together with (properly scaled) random initialization, ensures proximity to such an invariant set during training, allowing us to derive a novel non-asymptotic upper-bound on the distance between the trained network and the min-norm solution.

`@inproceedings{mtvm2021icml, abstract = {Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon is to study how initialization and overparametrization affect convergence and implicit bias of training algorithms. In this paper, we present a novel analysis of single-hidden-layer linear networks trained under gradient flow, which connects initialization, optimization, and overparametrization. Firstly, we show that the squared loss converges exponentially to its optimum at a rate that depends on the level of imbalance of the initialization. Secondly, we show that proper initialization constrains the dynamics of the network parameters to lie within an invariant set. In turn, minimizing the loss over this set leads to the min-norm solution. Finally, we show that large hidden layer width, together with (properly scaled) random initialization, ensures proximity to such an invariant set during training, allowing us to derive a novel non-asymptotic upper-bound on the distance between the trained network and the min-norm solution. }, author = {Min, Hancheng and Tarmoun, Salma and Vidal, Rene and Mallada, Enrique}, booktitle = {International Conference of Machine Learning (ICML)}, month = {5}, note = {(21.5$%$ acceptance)}, pages = {1-9}, pubstate = {accepted}, title = {On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks}, url = {https://mallada.ece.jhu.edu/pubs/2021-ICML-MTVM.pdf}, year = {2021} }`

- A. Castellano, J. Bazerque, and E. Mallada, “Learning to be safe, in finite time,” in American Control Conference, 2021, pp. 1-8.

[BibTeX] [Abstract] [Download PDF]This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one is willing to relax its optimality requirements mildly. We focus on the canonical multi-armed bandit problem and seek to study the exploration-preservation trade-off intrinsic within safe learning. More precisely, by defining a handicap metric that counts the number of unsafe actions, we provide an algorithm for discarding unsafe machines (or actions), with probability one, that achieves constant handicap. Our algorithm is rooted in the classical sequential probability ratio test, redefined here for continuing tasks. Under standard assumptions on sufficient exploration, our rule provably detects all unsafe machines in an (expected) finite number of rounds. The analysis also unveils a trade-off between the number of rounds needed to secure the environment and the probability of discarding safe machines. Our decision rule can wrap around any other algorithm to optimize a specific auxiliary goal since it provides a safe environment to search for (approximately) optimal policies. Simulations corroborate our theoretical findings and further illustrate the aforementioned trade-offs.

`@inproceedings{cbm2021acc, abstract = {This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one is willing to relax its optimality requirements mildly. We focus on the canonical multi-armed bandit problem and seek to study the exploration-preservation trade-off intrinsic within safe learning. More precisely, by defining a handicap metric that counts the number of unsafe actions, we provide an algorithm for discarding unsafe machines (or actions), with probability one, that achieves constant handicap. Our algorithm is rooted in the classical sequential probability ratio test, redefined here for continuing tasks. Under standard assumptions on sufficient exploration, our rule provably detects all unsafe machines in an (expected) finite number of rounds. The analysis also unveils a trade-off between the number of rounds needed to secure the environment and the probability of discarding safe machines. Our decision rule can wrap around any other algorithm to optimize a specific auxiliary goal since it provides a safe environment to search for (approximately) optimal policies. Simulations corroborate our theoretical findings and further illustrate the aforementioned trade-offs.}, author = {Castellano, Agustin and Bazerque, Juan and Mallada, Enrique}, booktitle = {American Control Conference}, grants = {CPS-1544771, CAREER-1752362, TRIPODS-1934979}, month = {1}, pages = {1-8}, pubstate = {accepted}, record = {submitted Sep. 2020}, title = {Learning to be safe, in finite time}, url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-CBM.pdf}, year = {2021} }`

- P. You and E. Mallada, “Saddle Flow Dynamics: Observable Certificates and Separable Regularization,” in American Control Conference, 2021, pp. 1-7.

[BibTeX] [Abstract] [Download PDF]This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and the equilibrium set in a LaSalle argument, and generalizes conventional conditions such as strict convexity-concavity and proximal regularization. We further build upon this certificate to propose a separable regularization method for saddle flow dynamics that makes minimal requirements on convexityconcavity and yet still guarantees asymptotic convergence to a saddle point. Our results generalize to saddle flow dynamics with projections on the vector field and have an immediate application as a distributed solution to linear programs.

`@inproceedings{ym2021acc, abstract = {This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and the equilibrium set in a LaSalle argument, and generalizes conventional conditions such as strict convexity-concavity and proximal regularization. We further build upon this certificate to propose a separable regularization method for saddle flow dynamics that makes minimal requirements on convexityconcavity and yet still guarantees asymptotic convergence to a saddle point. Our results generalize to saddle flow dynamics with projections on the vector field and have an immediate application as a distributed solution to linear programs.}, author = {You, Pengcheng and Mallada, Enrique}, booktitle = {American Control Conference}, grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979}, month = {1}, pages = {1-7}, pubstate = {accepted}, record = {submitted Sep. 2020}, title = {Saddle Flow Dynamics: Observable Certificates and Separable Regularization}, url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-YM.pdf}, year = {2021} }`

- M. D. Kaba, C. You, D. R. Robinson, E. Mallada, and R. Vidal, “A Nullspace Property for Subspace-Preserving Recovery,” in International Conference of Machine Learning (ICML), 2021, pp. 1-9.

[BibTeX] [Abstract] [Download PDF]Much of the theory for classical sparse recovery is based on conditions on the dictionary that are both necessary and sufficient (e.g., nullspace property) or only sufficient (e.g., incoherence and restricted isometry). In contrast, much of the theory for subspace-preserving recovery, the theoretical underpinnings for sparse subspace classification and clustering methods, is based on conditions on the subspaces and the data that are only sufficient (e.g., subspace incoherence and data inner-radius). This paper derives a necessary and sufficient condition for subspace-preserving recovery that is inspired by the classical nullspace property. Based on this novel condition, called here subspace nullspace property, we derive equivalent characterizations that either admit a clear geometric interpretation, relating data distribution and subspace separation to the recovery success, or can be verified using a finite set of extreme points of a properly defined set. We further exploit these characterizations to derive new sufficient conditions, based on inner-radius and outer-radius measures and dual bounds, that generalize existing conditions, while preserving the geometric interpretations. These results fill an important gap in the subspace-preserving recovery literature

`@inproceedings{kcrmv2021icml, abstract = {Much of the theory for classical sparse recovery is based on conditions on the dictionary that are both necessary and sufficient (e.g., nullspace property) or only sufficient (e.g., incoherence and restricted isometry). In contrast, much of the theory for subspace-preserving recovery, the theoretical underpinnings for sparse subspace classification and clustering methods, is based on conditions on the subspaces and the data that are only sufficient (e.g., subspace incoherence and data inner-radius). This paper derives a necessary and sufficient condition for subspace-preserving recovery that is inspired by the classical nullspace property. Based on this novel condition, called here subspace nullspace property, we derive equivalent characterizations that either admit a clear geometric interpretation, relating data distribution and subspace separation to the recovery success, or can be verified using a finite set of extreme points of a properly defined set. We further exploit these characterizations to derive new sufficient conditions, based on inner-radius and outer-radius measures and dual bounds, that generalize existing conditions, while preserving the geometric interpretations. These results fill an important gap in the subspace-preserving recovery literature}, author = {Kaba, Mustafa Devrim and You, Chong and Robinson, Daniel R. and Mallada, Enrique and Vidal, Rene}, booktitle = {International Conference of Machine Learning (ICML)}, month = {5}, note = {(21.5$%$ acceptance)}, pages = {1-9}, pubstate = {accepted}, title = {A Nullspace Property for Subspace-Preserving Recovery}, url = {https://mallada.ece.jhu.edu/pubs/2021-ICML-KCRMV.pdf}, year = {2021} }`

- Y. Jiang, A. Bernstein, P. Vorobev, and E. Mallada, “Grid-forming frequency shaping control in low inertia power systems,” in American Control Conference, 2021, pp. 1-6.

[BibTeX] [Abstract] [Download PDF]`@inproceedings{jbvm2021acc, abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.}, author = {Jiang, Yan and Bernstein, Andrey and Vorobev, Petr and Mallada, Enrique}, booktitle = {American Control Conference}, grants = {CAREER-1752362, AMPS-1736448, TRIPODS-1934979, EPCN-1711188}, month = {1}, pages = {1-6}, pubstate = {accepted}, record = {submitted Sep. 2020}, title = {Grid-forming frequency shaping control in low inertia power systems}, url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-JBVM.pdf}, year = {2021} }`

- Y. Shen, M. Bichuch, and E. Mallada, “On the Value of Energy Storage in Generation Cost Reduction,” in 19th IEEE European Control Conference (ECC), 2020, pp. 1526-1532.

[BibTeX] [Abstract] [Download PDF]This work seeks to quantify the benefits of using energy storage toward the reduction of the energy generation cost of a power system. A two-fold optimization framework is provided where the first optimization problem seeks to find the optimal storage schedule that minimizes operational costs. Since the operational cost depends on the storage capacity, a second optimization problem is then formulated with the aim of finding the optimal storage capacity to be deployed. Although, in general, these problems are difficult to solve, we provide a lower bound on the cost savings for a parametrized family of demand profiles. The optimization framework is numerically illustrated using real-world demand data from ISO New England. Numerical results show that energy storage can reduce energy generation costs by at least 2.5 percent.

`@inproceedings{sbm2020ecc, abstract = {This work seeks to quantify the benefits of using energy storage toward the reduction of the energy generation cost of a power system. A two-fold optimization framework is provided where the first optimization problem seeks to find the optimal storage schedule that minimizes operational costs. Since the operational cost depends on the storage capacity, a second optimization problem is then formulated with the aim of finding the optimal storage capacity to be deployed. Although, in general, these problems are difficult to solve, we provide a lower bound on the cost savings for a parametrized family of demand profiles. The optimization framework is numerically illustrated using real-world demand data from ISO New England. Numerical results show that energy storage can reduce energy generation costs by at least 2.5 percent.}, author = {Shen, Yue and Bichuch, Maxim and Mallada, Enrique}, booktitle = {19th IEEE European Control Conference (ECC)}, grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092}, keywords = {Power Networks}, month = {5}, pages = {1526-1532}, title = {On the Value of Energy Storage in Generation Cost Reduction}, url = {https://mallada.ece.jhu.edu/pubs/2020-ECC-SBM.pdf}, year = {2020} }`

- T. Zheng, J. W. Simpson-Porco, and E. Mallada, “Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach,” in American Control Conference, 2020, pp. 4677-4682. doi:10.23919/ACC45564.2020.9147997

[BibTeX] [Abstract] [Download PDF]We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints.

`@inproceedings{zsm2020acc, abstract = { We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints.}, author = {Zheng, Tianqi and Simpson-Porco, John W. and Mallada, Enrique}, booktitle = {American Control Conference}, doi = {10.23919/ACC45564.2020.9147997}, grants = {CPS-1544771, CAREER-1752362, ARO-W911NF-17-1-0092}, month = {7}, pages = {4677-4682}, title = {Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach}, url = {https://mallada.ece.jhu.edu/pubs/2020-ACC-ZSM.pdf}, year = {2020} }`

- J. Guthrie and E. Mallada, “Minimum-Time Charging of Energy Storage in Microgrids via Approximate Conic Relaxation,” in 19th IEEE European Control Conference (ECC), 2020, pp. 1713-1718.

[BibTeX] [Abstract] [Download PDF]We study the problem of maximizing energy transfer to a load in a DC microgrid while respecting constraints on bus voltages and currents, and accounting for the impact of neighboring constant power loads. Both the objective and dynamics give rise to indefinite quadratic terms, resulting in a non-convex optimization problem. Through change of variables and relaxations we develop a closely related second-order cone program. The problem retains the same feasible set as the original problem but utilizes a linear approximation of the non-convex objective. We demonstrate how this can be used to design approximately optimal charging profiles for periodic pulsed loads in real time.

`@inproceedings{gm2020ecc, abstract = {We study the problem of maximizing energy transfer to a load in a DC microgrid while respecting constraints on bus voltages and currents, and accounting for the impact of neighboring constant power loads. Both the objective and dynamics give rise to indefinite quadratic terms, resulting in a non-convex optimization problem. Through change of variables and relaxations we develop a closely related second-order cone program. The problem retains the same feasible set as the original problem but utilizes a linear approximation of the non-convex objective. We demonstrate how this can be used to design approximately optimal charging profiles for periodic pulsed loads in real time.}, author = {Guthrie, James and Mallada, Enrique}, booktitle = {19th IEEE European Control Conference (ECC)}, grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092}, keywords = {Power Networks}, month = {5}, pages = {1713-1718}, title = {Minimum-Time Charging of Energy Storage in Microgrids via Approximate Conic Relaxation}, url = {https://mallada.ece.jhu.edu/pubs/2020-ECC-GM-b.pdf}, year = {2020} }`

- L. Yang, M. H. Hajiesmaili, R. Sitaraman, A. Wierman, E. Mallada, and W. S. Wong, “Online Linear Optimization with Inventory Management Constraints,” in ACM Sigmetrics, 2020. doi:10.1145/3393691.3394207

[BibTeX] [Abstract] [Download PDF]This paper considers the problem of online linear optimization with inventory management constraints. Specifically, we consider an online scenario where a decision maker needs to satisfy her time-varying demand for some units of an asset, either from a market with a time-varying price or from her own inventory. In each time slot, the decision maker is presented a (linear) price and must immediately decide the amount to purchase for covering the demand and/or for storing in the inventory for future use. The inventory has a limited capacity and can be used to buy and store assets at low price and cover the demand when the price is high. The ultimate goal of the decision maker is to cover the demand at each time slot while minimizing the cost of buying assets from the market. We propose ARP, an online algorithm for linear programming with inventory constraints, and ARPRate, an extended version that handles rate constraints to/from the inventory. Both ARP and ARPRate achieve optimal competitive ratios, meaning that no other online algorithm can achieve a better theoretical guarantee. To illustrate the results, we use the proposed algorithms in a case study focused on energy procurement and storage management strategies for data centers.

`@inproceedings{yhswmw2020sigmetrics, abstract = {This paper considers the problem of online linear optimization with inventory management constraints. Specifically, we consider an online scenario where a decision maker needs to satisfy her time-varying demand for some units of an asset, either from a market with a time-varying price or from her own inventory. In each time slot, the decision maker is presented a (linear) price and must immediately decide the amount to purchase for covering the demand and/or for storing in the inventory for future use. The inventory has a limited capacity and can be used to buy and store assets at low price and cover the demand when the price is high. The ultimate goal of the decision maker is to cover the demand at each time slot while minimizing the cost of buying assets from the market. We propose ARP, an online algorithm for linear programming with inventory constraints, and ARPRate, an extended version that handles rate constraints to/from the inventory. Both ARP and ARPRate achieve optimal competitive ratios, meaning that no other online algorithm can achieve a better theoretical guarantee. To illustrate the results, we use the proposed algorithms in a case study focused on energy procurement and storage management strategies for data centers.}, author = {Yang, Lin and Hajiesmaili, Mohammad H. and Sitaraman, Ramesh and Wierman, Adam and Mallada, Enrique and Wong, Wing S.}, booktitle = {ACM Sigmetrics}, doi = {10.1145/3393691.3394207}, grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448,EPCN-1711188,}, month = {6}, title = {Online Linear Optimization with Inventory Management Constraints}, url = {https://mallada.ece.jhu.edu/pubs/2020-Sigmetrics-YHSWMW.pdf}, year = {2020} }`

- H. Min and E. Mallada, “Dynamics Concentration of Tightly-Connected Large-Scale Networks,” in 58th IEEE Conference on Decision and Control (CDC), 2019, pp. 758-763. doi:10.1109/CDC40024.2019.9029796

[BibTeX] [Abstract] [Download PDF]The ability to achieve coordinated behavior –engineered or emergent– on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the conditions under which agents within a network can reach agreement (consensus) or develop coordinated behaviors such as synchronization. However, fewer advances have been made toward explaining another commonly observed phenomena in tightly-connected networks systems: output responses of nodes in the networks are almost identical to each other despite heterogeneity in their individual dynamics. In this paper, we leverage tools from high-dimensional probability to provide an initial answer to this phenomena. More precisely, we show that for linear networks of nodal random transfer functions, as the networks size and connectivity grows, every node in the network follows the same response to an input or disturbance — irrespectively of the source of this input. We term this behavior as dynamics concentration as it stems from the fact that the network transfer matrix uniformly converges in probability to a unique dynamic response –i.e., it concentrates– determined by the distribution of the random transfer function of each node. We further discuss the implications of our analysis in the context of model reduction and robustness, and provide numerical evidence that similar phenomena occur in small deterministic networks over a properly defined frequency band.

`@inproceedings{mm2019cdc, abstract = {The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the conditions under which agents within a network can reach agreement (consensus) or develop coordinated behaviors such as synchronization. However, fewer advances have been made toward explaining another commonly observed phenomena in tightly-connected networks systems: output responses of nodes in the networks are almost identical to each other despite heterogeneity in their individual dynamics. In this paper, we leverage tools from high-dimensional probability to provide an initial answer to this phenomena. More precisely, we show that for linear networks of nodal random transfer functions, as the networks size and connectivity grows, every node in the network follows the same response to an input or disturbance -- irrespectively of the source of this input. We term this behavior as dynamics concentration as it stems from the fact that the network transfer matrix uniformly converges in probability to a unique dynamic response --i.e., it concentrates-- determined by the distribution of the random transfer function of each node. We further discuss the implications of our analysis in the context of model reduction and robustness, and provide numerical evidence that similar phenomena occur in small deterministic networks over a properly defined frequency band.}, author = {Min, Hancheng and Mallada, Enrique}, booktitle = {58th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC40024.2019.9029796}, grants = {ARO-W911NF-17-1-0092, CPS-1544771, EPCN-1711188, CAREER-1752362, AMPS-1736448, ENERGISE-DE-EE0008006}, month = {12}, pages = {758-763}, title = {Dynamics Concentration of Tightly-Connected Large-Scale Networks}, url = {https://mallada.ece.jhu.edu/pubs/2019-CDC-MM.pdf}, year = {2019} }`

- P. You, D. F. Gayme, and E. Mallada, “The Role of Strategic Load Participants in Two-Stage Settlement Electricity Markets,” in 58th IEEE Conference on Decision and Control (CDC), 2019, pp. 8416-8422. doi:10.1109/CDC40024.2019.9029514

[BibTeX] [Abstract] [Download PDF]We consider the problem of designing a feedback controller that guides the input and output of a linear timeinvariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance, piecewise constant in time, which shifts the feasible set defined by the system equilibrium constraints. Our proposed design combines proportional-integral control with gradient feedback, and enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in steady-state, and provide a stability criterion based on absolute stability theory. The effectiveness of our approach is illustrated on a simple example system.

`@inproceedings{ygm2019cdc, abstract = {We consider the problem of designing a feedback controller that guides the input and output of a linear timeinvariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance, piecewise constant in time, which shifts the feasible set defined by the system equilibrium constraints. Our proposed design combines proportional-integral control with gradient feedback, and enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in steady-state, and provide a stability criterion based on absolute stability theory. The effectiveness of our approach is illustrated on a simple example system.}, author = {You, Pengcheng and Gayme, Dennice F. and Mallada, Enrique}, booktitle = {58th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC40024.2019.9029514}, grants = {ARO-W911NF-17-1-0092, CPS-1544771, EPCN-1711188, CAREER-1752362, AMPS-1736448, ENERGISE-DE-EE0008006}, month = {12}, pages = {8416-8422}, title = {The Role of Strategic Load Participants in Two-Stage Settlement Electricity Markets}, url = {https://mallada.ece.jhu.edu/pubs/2019-CDC-YGM.pdf}, year = {2019} }`

- J. Guthrie and E. Mallada, “Adversarial Model Predictive Control via Second Order Cone Programming,” in 58th IEEE Conference on Decision and Control (CDC), 2019, pp. 1403-1409. doi:10.1109/CDC40024.2019.9029244

[BibTeX] [Abstract] [Download PDF]We study the problem of designing attacks to safety critical systems in which the adversary seeks to maximize the overall system cost within a model predictive control framework. Although in general this problem is NP-hard, we characterize a family of problems that can be solved in polynomial time via a second-order cone programming relaxation. In particular, we show that positive systems fall under this family. We provide examples demonstrating the design of optimal attacks on an autonomous vehicle and a microgrid.

`@inproceedings{gm2019cdc, abstract = {We study the problem of designing attacks to safety critical systems in which the adversary seeks to maximize the overall system cost within a model predictive control framework. Although in general this problem is NP-hard, we characterize a family of problems that can be solved in polynomial time via a second-order cone programming relaxation. In particular, we show that positive systems fall under this family. We provide examples demonstrating the design of optimal attacks on an autonomous vehicle and a microgrid.}, author = {Guthrie, James and Mallada, Enrique}, booktitle = {58th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC40024.2019.9029244}, grants = {ARO-W911NF-17-1-0092, CPS-1544771, EPCN-1711188, CAREER-1752362, AMPS-1736448}, month = {12}, pages = {1403-1409}, title = {Adversarial Model Predictive Control via Second Order Cone Programming}, url = {https://mallada.ece.jhu.edu/pubs/2019-CDC-GM.pdf}, year = {2019} }`

- C. Avraam, J. Rines, A. Sarker, F. Paganini, and E. Mallada, “Voltage Collapse Stabilization in Star DC Networks,” in American Control Conference, 2019, pp. 1957-1964. doi:10.23919/ACC.2019.8814708

[BibTeX] [Abstract] [Download PDF]Voltage collapse is a type of blackout-inducing dynamic instability that occurs when the power demand exceeds the maximum power that can be transferred through the network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficiencies as it prevents operators to fully utilize the network resources and does not account for unprescribed events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization. More precisely, for a DC network, we formulate the problem of voltage stability as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We show that such a system can be interpreted as a dynamic game, where each player (load) seeks to myopically maximize their utility, and where every stable power flow solution amounts to a Local Nash Equilibrium. Using this framework, we show that voltage collapse is equivalent to the non-existence of a Local Nash Equilibrium in the game and, as a result, it is caused by the lack of cooperation between loads. Finally, we propose a Voltage Collapse Stabilizer (VCS) controller that uses (flexible) loads that are willing to cooperate and provides a fair allocation of the curtailed demand. Our solution stabilizes voltage collapse even in the presence of non-cooperative loads. Numerical simulations validate several features of our controllers.

`@inproceedings{arspm2019acc, abstract = {Voltage collapse is a type of blackout-inducing dynamic instability that occurs when the power demand exceeds the maximum power that can be transferred through the network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficiencies as it prevents operators to fully utilize the network resources and does not account for unprescribed events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization. More precisely, for a DC network, we formulate the problem of voltage stability as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We show that such a system can be interpreted as a dynamic game, where each player (load) seeks to myopically maximize their utility, and where every stable power flow solution amounts to a Local Nash Equilibrium. Using this framework, we show that voltage collapse is equivalent to the non-existence of a Local Nash Equilibrium in the game and, as a result, it is caused by the lack of cooperation between loads. Finally, we propose a Voltage Collapse Stabilizer (VCS) controller that uses (flexible) loads that are willing to cooperate and provides a fair allocation of the curtailed demand. Our solution stabilizes voltage collapse even in the presence of non-cooperative loads. Numerical simulations validate several features of our controllers.}, author = {Avraam, Charalampos and Rines, Jesse and Sarker, Aurik and Paganini, Fernando and Mallada, Enrique}, booktitle = {American Control Conference}, doi = {10.23919/ACC.2019.8814708}, grants = {CAREER-1752362,EPCN-1711188,ENERGISE-DE-EE0008006,ARO-W911NF-17-1-0092,EPCN-1711188,CPS-1544771}, keywords = {Power Networks}, month = {06}, pages = {1957-1964}, title = {Voltage Collapse Stabilization in Star DC Networks}, url = {https://mallada.ece.jhu.edu/pubs/2019-ACC-ARSPM.pdf}, year = {2019} }`

- C. Ji, M. H. Hajiesmaili, D. F. Gayme, and E. Mallada, “Coordinating Distribution System Resources for Co-optimized Participation in Energy and Ancillary Service Transmission System Markets,” in American Control Conference, 2019, pp. 1315-1322. doi:10.23919/ACC.2019.8815242

[BibTeX] [Abstract] [Download PDF]This paper investigates the potential of using aggregate controllable loads and energy storage systems from multiple heterogeneous feeders to jointly optimize a utility’s energy procurement cost from the real-time market and their revenue from ancillary service markets. Toward this, we formulate an optimization problem that co-optimizes real-time and energy reserve markets based on real-time and ancillary service market prices, along with available solar power, storage and demand data from each of the feeders within a single distribution network. The optimization, which includes all network system constraints, provides real/reactive power and energy storage set-points for each feeder as well as a schedule for the aggregate system’s participation in the two types of markets. We evaluate the performance of our algorithm using several trace-driven simulations based on a real-world circuit of a New Jersey utility. The results demonstrate that active participation through controllable loads and storage significantly reduces the utility’s net costs, i.e., real-time energy procurement costs minus ancillary market revenues.

`@inproceedings{jhgm2019acc, abstract = {This paper investigates the potential of using aggregate controllable loads and energy storage systems from multiple heterogeneous feeders to jointly optimize a utility's energy procurement cost from the real-time market and their revenue from ancillary service markets. Toward this, we formulate an optimization problem that co-optimizes real-time and energy reserve markets based on real-time and ancillary service market prices, along with available solar power, storage and demand data from each of the feeders within a single distribution network. The optimization, which includes all network system constraints, provides real/reactive power and energy storage set-points for each feeder as well as a schedule for the aggregate system's participation in the two types of markets. We evaluate the performance of our algorithm using several trace-driven simulations based on a real-world circuit of a New Jersey utility. The results demonstrate that active participation through controllable loads and storage significantly reduces the utility's net costs, i.e., real-time energy procurement costs minus ancillary market revenues.}, author = {Ji, Chengda and Hajiesmaili, Mohammad H. and Gayme, Dennice F. and Mallada, Enrique}, booktitle = {American Control Conference}, doi = {10.23919/ACC.2019.8815242}, grants = {CAREER-1752362, ENERGISE-DE-EE0008006, EPCN-1711188}, month = {06}, pages = {1315-1322}, title = {Coordinating Distribution System Resources for Co-optimized Participation in Energy and Ancillary Service Transmission System Markets}, url = {https://mallada.ece.jhu.edu/pubs/2019-ACC-JHGM.pdf}, year = {2019} }`

- M. Zhao, M. D. Kaba, R. Vidal, D. R. Robinson, and E. Mallada, “Sparse Recovery over Graph Incidence Matrices,” in 57th IEEE Conference on Decision and Control (CDC), 2018, pp. 364-371. doi:10.1109/CDC.2018.8619666

[BibTeX] [Abstract] [Download PDF]Classical results in sparse representation guarantee the exact recovery of sparse signals under assumptions on the dictionary that are either too strong or NP hard to check. Moreover, such results may be too pessimistic in practice since they are based on a worst-case analysis. In this paper, we consider the sparse recovery of signals defined over a graph, for which the dictionary takes the form of an incidence matrix. We show that in this case necessary and sufficient conditions can be derived in terms of properties of the cycles of the graph, which can be checked in polynomial time. Our analysis further allows us to derive location dependent conditions for recovery that only depend on the cycles of the graph that intersect this support. Finally, we exploit sparsity properties on the measurements to a specialized sub-graph-based recovery algorithm that outperforms the standard $l_1$-minimization.

`@inproceedings{zkvrm2018cdc, abstract = {Classical results in sparse representation guarantee the exact recovery of sparse signals under assumptions on the dictionary that are either too strong or NP hard to check. Moreover, such results may be too pessimistic in practice since they are based on a worst-case analysis. In this paper, we consider the sparse recovery of signals defined over a graph, for which the dictionary takes the form of an incidence matrix. We show that in this case necessary and sufficient conditions can be derived in terms of properties of the cycles of the graph, which can be checked in polynomial time. Our analysis further allows us to derive location dependent conditions for recovery that only depend on the cycles of the graph that intersect this support. Finally, we exploit sparsity properties on the measurements to a specialized sub-graph-based recovery algorithm that outperforms the standard $l_1$-minimization.}, author = {Zhao, Mengnan and Kaba, Mustafa Devrim and Vidal, Rene and Robinson, Daniel R. and Mallada, Enrique}, booktitle = {57th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2018.8619666}, grants = {AMPS:1736448}, issn = {2576-2370}, month = {12}, pages = {364-371}, title = {Sparse Recovery over Graph Incidence Matrices}, url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-ZKVRM.pdf}, year = {2018} }`

- C. Ji, E. Mallada, and D. Gayme, “Evaluating Robustness of Consensus Algorithms Under Measurement Error over Digraph,” in 57th IEEE Conference on Decision and Control (CDC), 2018, pp. 1238-1244. doi:10.1109/CDC.2018.8619283

[BibTeX] [Abstract] [Download PDF]Consensus algorithms constitute a powerful tool for computing average values or coordinating agents in many distributed applications. Unfortunately, the same property that allows this computation (i.e., the nontrivial nullspace of the state matrix) leads to unbounded state variance in the presence of measurement errors. In this work, we explore the trade-off between relative and absolute communication (feedback) in the presence of measurement errors. We evaluate the robustness of first and second order integrator systems under a parameterized family of controllers (homotopy) that continuously trade between relative and absolute feedback interconnections in terms of the H2 norm an appropriately defined inputoutput system. Our approach extends the previous H2 norm based analysis to systems with directed feedback interconnections whose underlying weighted graph Laplacians are diagonalizable. Our results indicate that any level of absolute communication is sufficient to achieve a finite H2 norm but that purely relative feedback can only achieve finite norms when the measurement error is not exciting subspace associated with the consensus state. Numerical examples demonstrate that smoothly reducing the proportion of relative feedback in double integrator systems smoothly decreases the system performance and that this performance degradation is more rapid systems with relative feedback in only the first state (position).

`@inproceedings{jmg2018cdc, abstract = {Consensus algorithms constitute a powerful tool for computing average values or coordinating agents in many distributed applications. Unfortunately, the same property that allows this computation (i.e., the nontrivial nullspace of the state matrix) leads to unbounded state variance in the presence of measurement errors. In this work, we explore the trade-off between relative and absolute communication (feedback) in the presence of measurement errors. We evaluate the robustness of first and second order integrator systems under a parameterized family of controllers (homotopy) that continuously trade between relative and absolute feedback interconnections in terms of the H2 norm an appropriately defined inputoutput system. Our approach extends the previous H2 norm based analysis to systems with directed feedback interconnections whose underlying weighted graph Laplacians are diagonalizable. Our results indicate that any level of absolute communication is sufficient to achieve a finite H2 norm but that purely relative feedback can only achieve finite norms when the measurement error is not exciting subspace associated with the consensus state. Numerical examples demonstrate that smoothly reducing the proportion of relative feedback in double integrator systems smoothly decreases the system performance and that this performance degradation is more rapid systems with relative feedback in only the first state (position).}, author = {Ji, Chengda and Mallada, Enrique and Gayme, Dennice}, booktitle = {57th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2018.8619283}, grants = {CPS:1544771, ARO:W911NF-17-1-0092, CAREER:1752362}, issn = {2576-2370}, month = {12}, pages = {1238-1244}, title = {Evaluating Robustness of Consensus Algorithms Under Measurement Error over Digraph}, url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-JMG.pdf}, year = {2018} }`

- L. S. P. Lawrence, Z. Nelson, E. Mallada, and J. W. Simpson-Porco, “Optimal Steady-State Control for Linear Time-Invariant Systems,” in 57th IEEE Conference on Decision and Control (CDC), 2018, pp. 3251-3257. doi:10.1109/CDC.2018.8619812

[BibTeX] [Abstract] [Download PDF]We consider the problem of designing a feedback controller that guides the input and output of a linear timeinvariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance, piecewise constant in time, which shifts the feasible set defined by the system equilibrium constraints. Our proposed design combines proportional-integral control with gradient feedback, and enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in steady-state, and provide a stability criterion based on absolute stability theory. The effectiveness of our approach is illustrated on a simple example system.

`@inproceedings{lnms2018cdc, abstract = {We consider the problem of designing a feedback controller that guides the input and output of a linear timeinvariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance, piecewise constant in time, which shifts the feasible set defined by the system equilibrium constraints. Our proposed design combines proportional-integral control with gradient feedback, and enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in steady-state, and provide a stability criterion based on absolute stability theory. The effectiveness of our approach is illustrated on a simple example system.}, author = {Lawrence, Liam S. P. and Nelson, Zachary and Mallada, Enrique and Simpson-Porco, John W.}, booktitle = {57th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2018.8619812}, grants = {CPS:1544771, ARO:W911NF-17-1-0092, CAREER:1752362}, issn = {2576-2370}, month = {12}, pages = {3251-3257}, title = {Optimal Steady-State Control for Linear Time-Invariant Systems}, url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-LNMS.pdf}, year = {2018} }`

- Z. Nelson and E. Mallada, “An integral quadratic constraint framework for steady state optimization of linear time invariant systems,” in American Control Conference, 2018. doi:10.23919/ACC.2018.8431231

[BibTeX] [Abstract] [Download PDF]Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear Time-Invariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. The proposed solution can be logically divided into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component computes an input to the LTI system that aims to drive the system toward the optimal steady-state. We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using integral quadratic constraints (IQCs), the proposed framework is able to translate input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed loop system. We illustrate the versatility of our framework using several examples.

`@inproceedings{nm2018acc, abstract = {Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear Time-Invariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. The proposed solution can be logically divided into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component computes an input to the LTI system that aims to drive the system toward the optimal steady-state. We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using integral quadratic constraints (IQCs), the proposed framework is able to translate input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed loop system. We illustrate the versatility of our framework using several examples.}, author = {Nelson, Zachary and Mallada, Enrique}, booktitle = {American Control Conference}, doi = {10.23919/ACC.2018.8431231}, grants = {1544771, W911NF-17-1-0092, 1711188}, issn = {2378-5861}, keywords = {Optimization, IQCs}, month = {06}, title = {An integral quadratic constraint framework for steady state optimization of linear time invariant systems}, url = {https://mallada.ece.jhu.edu/pubs/2018-ACC-NM.pdf}, year = {2018} }`

- E. Weitenberg, Y. Jiang, C. Zhao, E. Mallada, F. Dorfler, and C. De Persis, “Robust decentralized frequency control: A leaky integrator approach,” in 17th IEEE European Control Conference (ECC), 2018. doi:10.23919/ECC.2018.8550060

[BibTeX] [Download PDF]`@inproceedings{wjzmdd2018ecc, author = {Weitenberg, Erik and Jiang, Yan and Zhao, Changhong and Mallada, Enrique and Dorfler, Florian and De Persis, Claudio}, booktitle = {17th IEEE European Control Conference (ECC)}, doi = {10.23919/ECC.2018.8550060}, grants = {1544771, 1711188, 1736448}, keywords = {Power Networks}, month = {6}, title = {Robust decentralized frequency control: A leaky integrator approach}, url = {https://mallada.ece.jhu.edu/pubs/2018-ECC-WJZMDD.pdf}, year = {2018} }`

- R. Pates and E. Mallada, “Damping, Inertia, and Delay Robustness Trade-offs in Power Systems,” in 23rd International Symposium on Mathematical Theory of Networks and Systems, 2018.

[BibTeX] [Abstract] [Download PDF]Electro-mechanical oscillations in power systems are typically controlled by simple decentralised controllers. We derive a formula for computing the delay margin of such controllers when the power system is represented by a simple mechanical network. This formula reveals a clear trade-off between system damping, inertia, and robustness to delays. In particular, it shows that reducing system inertia, which is a common consequence of increased renewable generation, can reduce robustness to unmodelled dynamics.

`@inproceedings{pm2018mtns, abstract = {Electro-mechanical oscillations in power systems are typically controlled by simple decentralised controllers. We derive a formula for computing the delay margin of such controllers when the power system is represented by a simple mechanical network. This formula reveals a clear trade-off between system damping, inertia, and robustness to delays. In particular, it shows that reducing system inertia, which is a common consequence of increased renewable generation, can reduce robustness to unmodelled dynamics.}, author = {Pates, Richard and Mallada, Enrique}, booktitle = {23rd International Symposium on Mathematical Theory of Networks and Systems}, grants = {CPS:1544771, ARO:W911NF-17-1-0092, 1711188, CAREER:}, month = {7}, title = {Damping, Inertia, and Delay Robustness Trade-offs in Power Systems}, url = {https://mallada.ece.jhu.edu/pubs/2018-MTNS-PM.pdf}, year = {2018} }`

- Y. Jiang, R. Pates, and E. Mallada, “Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 5098-5105. doi:10.1109/CDC.2017.8264414

[BibTeX] [Abstract] [Download PDF]Implementing frequency response using grid-connected inverters is one of the popular proposed alternatives to mitigate the dynamic degradation experienced in low inertia power systems. However, such solution faces several challenges as inverters do not intrinsically possess the natural response to power fluctuations that synchronous generators have. Thus, to synthetically generate this response, inverters need to take frequency measurements, which are usually noisy, and subsequently make changes in the output power, which are therefore delayed. This paper explores the system-wide performance tradeoffs that arise when measurement noise, delayed actions, and power disturbances are considered in the design of dynamic controllers for grid-connected inverters. Using a recently proposed dynamic droop (iDroop) control for grid-connected inverters that is inspired by classical first order lead-lag compensation, we show that the sets of parameters that result in highest noise attenuation, power disturbance mitigation, and delay robustness do not necessarily have a common intersection. In particular, lead compensation is desired in systems where power disturbances are the predominant source of degradation, while lag compensation is a better alternative when the system is dominated by delays or frequency noise. Our analysis further shows that iDroop can outperform the standard droop alternative in both joint noise and disturbance mitigation, and delay robustness.

`@inproceedings{jpm2017cdc, abstract = {Implementing frequency response using grid-connected inverters is one of the popular proposed alternatives to mitigate the dynamic degradation experienced in low inertia power systems. However, such solution faces several challenges as inverters do not intrinsically possess the natural response to power fluctuations that synchronous generators have. Thus, to synthetically generate this response, inverters need to take frequency measurements, which are usually noisy, and subsequently make changes in the output power, which are therefore delayed. This paper explores the system-wide performance tradeoffs that arise when measurement noise, delayed actions, and power disturbances are considered in the design of dynamic controllers for grid-connected inverters. Using a recently proposed dynamic droop (iDroop) control for grid-connected inverters that is inspired by classical first order lead-lag compensation, we show that the sets of parameters that result in highest noise attenuation, power disturbance mitigation, and delay robustness do not necessarily have a common intersection. In particular, lead compensation is desired in systems where power disturbances are the predominant source of degradation, while lag compensation is a better alternative when the system is dominated by delays or frequency noise. Our analysis further shows that iDroop can outperform the standard droop alternative in both joint noise and disturbance mitigation, and delay robustness.}, author = {Jiang, Yan and Pates, Richard and Mallada, Enrique}, booktitle = {56th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2017.8264414}, grants = {1544771, 1711188, W911NF-17-1-0092}, keywords = {Power Networks}, month = {12}, pages = {5098-5105}, title = {Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems}, url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-JPM.pdf}, year = {2017} }`

- G. H. Oral, E. Mallada, and D. Gayme, “Performance of first and second order linear networked systems over digraphs,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 1688-1694. doi:10.1109/CDC.2017.8263893

[BibTeX] [Abstract] [Download PDF]In this paper we investigate the performance of linear networked dynamical systems over strongly connected digraphs. We consider first and second order systems subject to distributed disturbance inputs, and define an appropriate system output so that the performance measure is quantified through the input-output $\mathcal H_2$ norm of the system. We first develop a generalized framework for the computation of the $\mathcal H_2$ norm. We apply this framework to systems whose underlying network graphs result in normal weighted graph Laplacian matrices. We consider two performance metrics and find closed form solutions for the first and bounds for the other; which both depend on the eigenvalues of these graph Laplacians. Numerical examples indicate that: (i) the tightness of the bounds are highly dependent on the graph structure, (ii) the $\mathcal H_2$ norm of a symmetric system is less than or equal to that of the corresponding perturbed non-symmetric system for either line or complete graphs when the network size is sufficiently large.

`@inproceedings{omg2017cdc, abstract = {In this paper we investigate the performance of linear networked dynamical systems over strongly connected digraphs. We consider first and second order systems subject to distributed disturbance inputs, and define an appropriate system output so that the performance measure is quantified through the input-output $\mathcal H_2$ norm of the system. We first develop a generalized framework for the computation of the $\mathcal H_2$ norm. We apply this framework to systems whose underlying network graphs result in normal weighted graph Laplacian matrices. We consider two performance metrics and find closed form solutions for the first and bounds for the other; which both depend on the eigenvalues of these graph Laplacians. Numerical examples indicate that: (i) the tightness of the bounds are highly dependent on the graph structure, (ii) the $\mathcal H_2$ norm of a symmetric system is less than or equal to that of the corresponding perturbed non-symmetric system for either line or complete graphs when the network size is sufficiently large.}, author = {Oral, H. Giray and Mallada, Enrique and Gayme, Dennice}, booktitle = {56th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2017.8263893}, grants = {1544771, W911NF-17-1-0092}, keywords = {Power Networks}, month = {12}, pages = {1688-1694}, title = {Performance of first and second order linear networked systems over digraphs}, url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-OMG.pdf}, year = {2017} }`

- M. H. Hajiesmaili, D. Cai, and E. Mallada, “Understanding the Inefficiency of Security-Constrained Economic Dispatch,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 2035-2040. doi:10.1109/CDC.2017.8263947

[BibTeX] [Abstract] [Download PDF]The security-constrained economic dispatch (SCED) problem tries to maintain the reliability of a power network by ensuring that a single failure does not lead to a global outage. The previous research has mainly investigated SCED by formulating the problem in different modalities, e.g. preventive or corrective, and devising efficient solutions for SCED. In this paper, we tackle a novel and important direction, and analyze the economic cost of incorporating security constraints in economic dispatch. Inspired by existing inefficiency metrics in game theory and computer science, we introduce notion of price of security as a metric that formally characterizes the economic inefficiency of security-constrained economic dispatch as compared to the original problem without security constraints. Then, we focus on the preventive approach in a simple topology comprising two buses and two lines, and investigate the impact of generation availability and demand distribution on the price of security. Moreover, we explicitly derive the worst-case input instance that leads to the maximum price of security. By extensive experimental study on two test-cases, we verify the analytical results and provide insights for characterizing the price of security in general networks.

`@inproceedings{hcm2017cdc, abstract = {The security-constrained economic dispatch (SCED) problem tries to maintain the reliability of a power network by ensuring that a single failure does not lead to a global outage. The previous research has mainly investigated SCED by formulating the problem in different modalities, e.g. preventive or corrective, and devising efficient solutions for SCED. In this paper, we tackle a novel and important direction, and analyze the economic cost of incorporating security constraints in economic dispatch. Inspired by existing inefficiency metrics in game theory and computer science, we introduce notion of price of security as a metric that formally characterizes the economic inefficiency of security-constrained economic dispatch as compared to the original problem without security constraints. Then, we focus on the preventive approach in a simple topology comprising two buses and two lines, and investigate the impact of generation availability and demand distribution on the price of security. Moreover, we explicitly derive the worst-case input instance that leads to the maximum price of security. By extensive experimental study on two test-cases, we verify the analytical results and provide insights for characterizing the price of security in general networks.}, author = {Hajiesmaili, Mohammad H. and Cai, Desmond and Mallada, Enrique}, booktitle = {56th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2017.8263947}, grants = {1544771, 1711188, 1736448}, keywords = {Power Networks}, month = {12}, pages = {2035-2040}, title = {Understanding the Inefficiency of Security-Constrained Economic Dispatch}, url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-HCM.pdf}, year = {2017} }`

- F. Paganini and E. Mallada, “Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia,” in 55th Allerton Conference on Communication, Control, and Computing, 2017, pp. 324-331. doi:10.1109/ALLERTON.2017.8262755

[BibTeX] [Abstract] [Download PDF]A recent trend in control of power systems has sought to quantify the synchronization dynamics in terms of a global performance metric, compute it under very simplified assumptions, and use it to gain insight on the role of system parameters, in particular, inertia. In this paper, we wish to extend this approach to more realistic scenarios, by incorporating the heterogeneity of machine ratings, more complete machine models, and also to more closely map it to classical power engineering notions such as Nadir, Rate of Change of Frequency (RoCoF), and inter-area oscillations. We consider the system response to a step change in power excitation, and define the system frequency as a weighted average of generator frequencies (with weights proportional to each machine’s rating); we characterize Nadir and RoCoF by the Linf norm of the system frequency and its derivative, respectively, and inter-areas oscillations by the L2 norm of the error of the vector of bus frequencies w.r.t. the system frequency. For machine models where the dynamic parameters (inertia, damping, etc.) are proportional to rating, we analytically compute these norms and use them to show that the role of inertia is more nuanced than in the conventional wisdom. With the classical swing dynamics, inertia constant plays a secondary role in performance. It is only when the turbine dynamics are introduced that the benefits of inertia become more prominent.

`@inproceedings{pm2017allerton, abstract = {A recent trend in control of power systems has sought to quantify the synchronization dynamics in terms of a global performance metric, compute it under very simplified assumptions, and use it to gain insight on the role of system parameters, in particular, inertia. In this paper, we wish to extend this approach to more realistic scenarios, by incorporating the heterogeneity of machine ratings, more complete machine models, and also to more closely map it to classical power engineering notions such as Nadir, Rate of Change of Frequency (RoCoF), and inter-area oscillations. We consider the system response to a step change in power excitation, and define the system frequency as a weighted average of generator frequencies (with weights proportional to each machine's rating); we characterize Nadir and RoCoF by the Linf norm of the system frequency and its derivative, respectively, and inter-areas oscillations by the L2 norm of the error of the vector of bus frequencies w.r.t. the system frequency. For machine models where the dynamic parameters (inertia, damping, etc.) are proportional to rating, we analytically compute these norms and use them to show that the role of inertia is more nuanced than in the conventional wisdom. With the classical swing dynamics, inertia constant plays a secondary role in performance. It is only when the turbine dynamics are introduced that the benefits of inertia become more prominent.}, author = {Paganini, Fernando and Mallada, Enrique}, booktitle = {55th Allerton Conference on Communication, Control, and Computing}, doi = {10.1109/ALLERTON.2017.8262755}, grants = {1544771, 1711188, 1736448}, keywords = {Power Networks; Synchronization}, month = {10}, pages = {324-331}, title = {Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia}, url = {https://mallada.ece.jhu.edu/pubs/2017-Allerton-PM.pdf}, year = {2017} }`

- R. Pates and E. Mallada, “Decentralised Robust Inverter-based Control in Power Systems,” in IFAC World Congress, 2017, pp. 5548-5553. doi:https://doi.org/10.1016/j.ifacol.2017.08.1097

[BibTeX] [Abstract] [Download PDF]This paper develops a novel framework for power system stability analysis, that allows for the decentralised design of inverter based controllers. The method requires that each individual inverter satisfies a standard H1 design requirement. Critically each requirement depends only on the dynamics of the components and inverters at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The method is both robust to network and delay uncertainties, as well as heterogeneous network components, and when no network information is available it reduces to the standard decentralised passivity sufficient condition for stability. We illustrate the novelty and strength of our approach by studying the design of inverter-based control laws in the presence of delays.

`@inproceedings{pm2017ifac-wc, abstract = {This paper develops a novel framework for power system stability analysis, that allows for the decentralised design of inverter based controllers. The method requires that each individual inverter satisfies a standard H1 design requirement. Critically each requirement depends only on the dynamics of the components and inverters at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The method is both robust to network and delay uncertainties, as well as heterogeneous network components, and when no network information is available it reduces to the standard decentralised passivity sufficient condition for stability. We illustrate the novelty and strength of our approach by studying the design of inverter-based control laws in the presence of delays.}, author = {Pates, Richard and Mallada, Enrique}, booktitle = {IFAC World Congress}, doi = {https://doi.org/10.1016/j.ifacol.2017.08.1097}, grants = {1544771}, keywords = {Power Networks}, month = {7}, number = {1}, pages = {5548 - 5553}, title = {Decentralised Robust Inverter-based Control in Power Systems}, url = {https://mallada.ece.jhu.edu/pubs/2017-IFAC-WC-PM.pdf}, volume = {50}, year = {2017} }`

- M. H. Hajiesmaili, M. Chen, E. Mallada, and C. Chau, “Crowd-Sourced Storage-Assisted Demand Response in Microgrids,” in Proceedings of the Eighth International Conference on Future Energy Systems, New York, NY, USA, 2017, pp. 91-100. doi:10.1145/3077839.3077841

[BibTeX] [Abstract] [Download PDF]This paper studies the problem of utilizing heterogeneous energy storage systems, including electric vehicles and residential batteries, to perform demand-response in microgrids. The objective is to minimize the operational cost while fulfilling the demand-response requirement. The design space is to select and schedule a subset of available storage devices that are heterogeneous in operating cost, capacity, and availability in time. Designing a performance-optimized solution, however, is challenging due to the combinatorial nature of the problem with mixed packing and covering constraints, and the essential need for online solution design in practical scenarios where both demand-response requirement and the profile of user-owned storage systems arrive online. We tackle these challenges and design several online algorithms by leveraging a recent theoretical computer science technique which uses a problem-specific exponential potential function to solve online mixed packing and covering problems. We show that the fractional version of the algorithm achieves a logarithmic bi-criteria competitive ratio. Empirical trace-driven experiments demonstrate that our algorithms perform much better than the theoretical bounds and achieve close-to-optimal performance.

`@inproceedings{hcmc2017e-energy, abstract = {This paper studies the problem of utilizing heterogeneous energy storage systems, including electric vehicles and residential batteries, to perform demand-response in microgrids. The objective is to minimize the operational cost while fulfilling the demand-response requirement. The design space is to select and schedule a subset of available storage devices that are heterogeneous in operating cost, capacity, and availability in time. Designing a performance-optimized solution, however, is challenging due to the combinatorial nature of the problem with mixed packing and covering constraints, and the essential need for online solution design in practical scenarios where both demand-response requirement and the profile of user-owned storage systems arrive online. We tackle these challenges and design several online algorithms by leveraging a recent theoretical computer science technique which uses a problem-specific exponential potential function to solve online mixed packing and covering problems. We show that the fractional version of the algorithm achieves a logarithmic bi-criteria competitive ratio. Empirical trace-driven experiments demonstrate that our algorithms perform much better than the theoretical bounds and achieve close-to-optimal performance.}, acmid = {3077841}, address = {New York, NY, USA}, author = {Hajiesmaili, Mohammad H. and Chen, Minghua and Mallada, Enrique and Chau, Chi-Kin}, booktitle = {Proceedings of the Eighth International Conference on Future Energy Systems}, doi = {10.1145/3077839.3077841}, grants = {1544771, W911NF-17-1-0092}, isbn = {978-1-4503-5036-5}, keywords = {Microgrid, competitive online algorithm design, crowd-sourced storage-assisted demand response, scheduling}, location = {Shatin, Hong Kong}, month = {5}, numpages = {10}, pages = {91--100}, publisher = {ACM}, series = {e-Energy '17}, title = {Crowd-Sourced Storage-Assisted Demand Response in Microgrids}, url = {https://mallada.ece.jhu.edu/pubs/2017-eEnery-HCMC.pdf}, year = {2017} }`

- E. Mallada, “iDroop: A dynamic droop controller to decouple power grid’s steady-state and dynamic performance,” in 55th IEEE Conference on Decision and Control (CDC), 2016, pp. 4957-4964. doi:10.1109/CDC.2016.7799027

[BibTeX] [Abstract] [Download PDF]This paper presents a novel Dynam-i-c Droop (iDroop) control mechanism to perform primary frequency control with gird-connected inverters that improves the network dynamic performance while maintaining the same steady-state characteristics of droop control. The work is motivated by the increasing dynamic degradation experienced by the power grid due to the increment on asynchronous inverted-based generation. We show that the widely suggested virtual inertia solution suffers from unbounded noise amplification (infinite H2 norm) and therefore could potentially degrade further the grid performance once widely deployed. This motivates the proposed solution on this paper that over- comes the limitations of virtual inertia controllers while sharing the same advantages of traditional droop control. In particular, our iDroop controllers are decentralized, rebalance supply and demand, and provide power sharing. Furthermore, our solution improves the dynamic performance without affecting the steady state solution. Our algorithm can be incrementally deployed and can be guaranteed to be stable using a decentralized sufficient stability condition on the parameter values. We illustrate several features of our solution using numerical simulations.

`@inproceedings{m2016cdc, abstract = {This paper presents a novel Dynam-i-c Droop (iDroop) control mechanism to perform primary frequency control with gird-connected inverters that improves the network dynamic performance while maintaining the same steady-state characteristics of droop control. The work is motivated by the increasing dynamic degradation experienced by the power grid due to the increment on asynchronous inverted-based generation. We show that the widely suggested virtual inertia solution suffers from unbounded noise amplification (infinite H2 norm) and therefore could potentially degrade further the grid performance once widely deployed. This motivates the proposed solution on this paper that over- comes the limitations of virtual inertia controllers while sharing the same advantages of traditional droop control. In particular, our iDroop controllers are decentralized, rebalance supply and demand, and provide power sharing. Furthermore, our solution improves the dynamic performance without affecting the steady state solution. Our algorithm can be incrementally deployed and can be guaranteed to be stable using a decentralized sufficient stability condition on the parameter values. We illustrate several features of our solution using numerical simulations.}, author = {Mallada, Enrique}, booktitle = {55th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2016.7799027}, grants = {1544771}, keywords = {Power Networks}, month = {12}, pages = {4957-4964}, title = {iDroop: A dynamic droop controller to decouple power grid's steady-state and dynamic performance}, url = {https://mallada.ece.jhu.edu/pubs/2016-CDC-M.pdf}, year = {2016} }`

- A. Cherukuri, E. Mallada, S. H. Low, and J. Cortes, “The role of strong convexity-concavity in the convergence and robustness of the saddle-point dynamics,” in 54th Allerton Conference on Communication, Control, and Computing, 2016, pp. 504-510. doi:10.1109/ALLERTON.2016.7852273

[BibTeX] [Abstract] [Download PDF]This paper studies the projected saddle-point dynamics for a twice differentiable convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We provide a novel characterization of the omega-limit set of the trajectories of these dynamics in terms of the diagonal Hessian blocks of the saddle function. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexityconcavity of the saddle function. If this property is global, and for the case when the saddle function takes the form of the Lagrangian of an equality constrained optimization problem, we establish the input-to-state stability of the saddlepoint dynamics by providing an ISS Lyapunov function. Various examples illustrate our results.

`@inproceedings{cmlc2016allerton, abstract = {This paper studies the projected saddle-point dynamics for a twice differentiable convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We provide a novel characterization of the omega-limit set of the trajectories of these dynamics in terms of the diagonal Hessian blocks of the saddle function. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexityconcavity of the saddle function. If this property is global, and for the case when the saddle function takes the form of the Lagrangian of an equality constrained optimization problem, we establish the input-to-state stability of the saddlepoint dynamics by providing an ISS Lyapunov function. Various examples illustrate our results.}, author = {Ashish Cherukuri and Mallada, Enrique and Steven H. Low and Jorge Cortes}, booktitle = {54th Allerton Conference on Communication, Control, and Computing}, doi = {10.1109/ALLERTON.2016.7852273}, grants = {1544771}, keywords = {Saddle-Point Dynamics; Caratheodory solutions}, month = {09}, pages = {504-510}, title = {The role of strong convexity-concavity in the convergence and robustness of the saddle-point dynamics}, url = {https://mallada.ece.jhu.edu/pubs/2016-Allerton-CMLC.pdf}, year = {2016} }`

- C. Zhao, E. Mallada, S. H. Low, and J. W. Bialek, “A Unified Framework for Frequency Control and Congestion Management,” in Power Systems Computation Conference, 2016, pp. 1-7. doi:10.1109/PSCC.2016.7541028

[BibTeX] [Abstract] [Download PDF]The existing frequency control framework in power systems is challenged by lower inertia and more volatile power injections. We propose a new framework for frequency control and congestion management. We formulate an optimization problem that rebalances power, restores the nominal frequency, restores inter-area flows and maintains line flows below their limits in a way that minimizes the control cost. The cost can be squared deviations from the reference generations, minimizing the disruption from the last optimal dispatch. Our control thus maintains system security without interfering with the market operation. By deriving a primal-dual algorithm to solve this optimization, we design a completely decentralized primary frequency control without the need for explicit communication among the participating agents, and a distributed unified control which integrates primary and secondary frequency control and congestion management. Simulations show that the unified control not only achieves all the desired control goals in system equilibrium, but also improves the transient compared to traditional control schemes.

`@inproceedings{zmlb2016pscc, abstract = {The existing frequency control framework in power systems is challenged by lower inertia and more volatile power injections. We propose a new framework for frequency control and congestion management. We formulate an optimization problem that rebalances power, restores the nominal frequency, restores inter-area flows and maintains line flows below their limits in a way that minimizes the control cost. The cost can be squared deviations from the reference generations, minimizing the disruption from the last optimal dispatch. Our control thus maintains system security without interfering with the market operation. By deriving a primal-dual algorithm to solve this optimization, we design a completely decentralized primary frequency control without the need for explicit communication among the participating agents, and a distributed unified control which integrates primary and secondary frequency control and congestion management. Simulations show that the unified control not only achieves all the desired control goals in system equilibrium, but also improves the transient compared to traditional control schemes.}, author = {Zhao, Changhong and Mallada, Enrique and Low, Steven H and Bialek, Janusz W}, booktitle = {Power Systems Computation Conference}, doi = {10.1109/PSCC.2016.7541028}, keywords = {Power Networks; Frequency Control; Congestion Management}, month = {06}, pages = {1--7}, title = {A Unified Framework for Frequency Control and Congestion Management}, url = {https://mallada.ece.jhu.edu/pubs/2016-PSCC-ZMLB.pdf}, year = {2016} }`

- D. Cai, E. Mallada, and A. Wierman, “Distributed optimization decomposition for joint economic dispatch and frequency regulation,” in 54th IEEE Conference on Decision and Control (CDC), 2015, pp. 15-22. doi:10.1109/CDC.2015.7402081

[BibTeX] [Abstract] [Download PDF]Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co- optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

`@inproceedings{cmw2015cdc, abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co- optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.}, author = {Cai, Desmond and Mallada, Enrique and Wierman, Adam}, booktitle = {54th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2015.7402081}, keywords = {Power Networks;Markets; Optimization}, month = {12}, pages = {15-22}, title = {Distributed optimization decomposition for joint economic dispatch and frequency regulation}, url = {https://mallada.ece.jhu.edu/pubs/2015-CDC-CMW.pdf}, web = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7402081}, year = {2015} }`

- C. Zhao, E. Mallada, and F. Dorfler, “Distributed frequency control for stability and economic dispatch in power networks,” in American Control Conference, 2015, pp. 2359-2364. doi:10.1109/ACC.2015.7171085

[BibTeX] [Abstract] [Download PDF]We explore two different frequency control strategies to ensure stability of power networks and achieve economic dispatch between generators and controllable loads. We first show the global asymptotic stability of a completely decentralized frequency integral control. Then we design a distributed averaging-based integral (DAI) control which operates by local frequency sensing and neighborhood communication. Equilibrium analysis shows that DAI recovers nominal frequency with minimum total generation cost and user disutility for load control after a change in generation or load. Local asymptotic stability of DAI is established with a Lyapunov method. Simulations demonstrate improvement in both transient and steady state performance achieved by the proposed control strategies, compared to droop control.

`@inproceedings{zmd2015acc, abstract = {We explore two different frequency control strategies to ensure stability of power networks and achieve economic dispatch between generators and controllable loads. We first show the global asymptotic stability of a completely decentralized frequency integral control. Then we design a distributed averaging-based integral (DAI) control which operates by local frequency sensing and neighborhood communication. Equilibrium analysis shows that DAI recovers nominal frequency with minimum total generation cost and user disutility for load control after a change in generation or load. Local asymptotic stability of DAI is established with a Lyapunov method. Simulations demonstrate improvement in both transient and steady state performance achieved by the proposed control strategies, compared to droop control.}, author = {Zhao, Changhong and Mallada, Enrique and Dorfler, Florian}, booktitle = {American Control Conference}, doi = {10.1109/ACC.2015.7171085}, keywords = {Power Networks; Synchronization}, month = {07}, pages = {2359--2364}, title = {Distributed frequency control for stability and economic dispatch in power networks}, url = {https://mallada.ece.jhu.edu/pubs/2015-ACC-ZMD.pdf}, web = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7171085}, year = {2015} }`

- A. Cherukuri, E. Mallada, and J. Cortes, “Convergence of Caratheodory solutions for primal-dual dynamics in constrained concave optimization,” in SIAM Conference on Control and its Applications, 2015. doi:10.1137/1.9781611974072.40

[BibTeX] [Abstract] [Download PDF]This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and establish their existence, uniqueness, and continuity with respect to the initial conditions. We employ the invariance principle for Caratheodory solutions of a discontinuous dynamical system to show that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.

`@inproceedings{cmc2015siam-ct, abstract = {This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and establish their existence, uniqueness, and continuity with respect to the initial conditions. We employ the invariance principle for Caratheodory solutions of a discontinuous dynamical system to show that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.}, author = {Cherukuri, Ashish and Mallada, Enrique and Cortes, Jorge}, booktitle = {SIAM Conference on Control and its Applications}, doi = {10.1137/1.9781611974072.40}, keywords = {Saddle-Point Dynamics; Caratheodory solutions}, month = {07}, title = {Convergence of Caratheodory solutions for primal-dual dynamics in constrained concave optimization}, url = {https://mallada.ece.jhu.edu/pubs/2015-SIAM-CT-CMC.pdf}, web = {http://epubs.siam.org/doi/abs/10.1137/1.9781611974072.40}, year = {2015} }`

- A. Gushchin, E. Mallada, and A. Tang, “Synchronization of heterogeneous Kuramoto oscillators with arbitrary topology,” in American Control Conference, 2015. doi:10.1109/ACC.2015.7170807

[BibTeX] [Abstract] [Download PDF]We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a Positively Invariant Set (PIS) and lead to synchronization. Unlike previous works that focus only on analytical bounds, here we introduce an optimization approach to provide a computational-analytical bound that can further exploit the particular features of each individual system such as topology and frequency distribution. Examples are provided to illustrate our results as well as the improvement over previous existing bounds.

`@inproceedings{gmt2015acc, abstract = {We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a Positively Invariant Set (PIS) and lead to synchronization. Unlike previous works that focus only on analytical bounds, here we introduce an optimization approach to provide a computational-analytical bound that can further exploit the particular features of each individual system such as topology and frequency distribution. Examples are provided to illustrate our results as well as the improvement over previous existing bounds.}, author = {Gushchin, Andrey and Mallada, Enrique and Tang, Ao}, booktitle = {American Control Conference}, doi = {10.1109/ACC.2015.7170807}, keywords = {Coupled Oscillators; Synchronization}, month = {07}, title = {Synchronization of heterogeneous Kuramoto oscillators with arbitrary topology}, url = {https://mallada.ece.jhu.edu/pubs/2015-ACC-GMT.pdf}, web = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7170807}, year = {2015} }`

- A. Gushchin, E. Mallada, and A. Tang, “Synchronization of heterogeneous Kuramoto oscillators with graphs of diameter two,” in Conference on Information Sciences and Systems, 2015. doi:10.1109/CISS.2015.7086426

[BibTeX] [Abstract] [Download PDF]In this article we study synchronization of Kuramoto oscillators with heterogeneous frequencies, and where underlying topology is a graph of diameter two. When the coupling strengths between every two connected oscillators are the same, we find an analytic condition that guarantees an existence of a Positively Invariant Set (PIS) and demonstrate that existence of a PIS suffices for frequency synchronization. For graphs of diameter two, this synchronization condition is significantly better than existing general conditions for an arbitrary topology. If the coupling strengths can be different for different pairs of connected oscillators, we formulate an optimization problem that finds sufficient for synchronization coupling strengths such that their sum is minimal.

`@inproceedings{gmt2015ciss, abstract = {In this article we study synchronization of Kuramoto oscillators with heterogeneous frequencies, and where underlying topology is a graph of diameter two. When the coupling strengths between every two connected oscillators are the same, we find an analytic condition that guarantees an existence of a Positively Invariant Set (PIS) and demonstrate that existence of a PIS suffices for frequency synchronization. For graphs of diameter two, this synchronization condition is significantly better than existing general conditions for an arbitrary topology. If the coupling strengths can be different for different pairs of connected oscillators, we formulate an optimization problem that finds sufficient for synchronization coupling strengths such that their sum is minimal.}, author = {Gushchin, Andrey and Mallada, Enrique and Tang, Ao}, booktitle = {Conference on Information Sciences and Systems}, doi = {10.1109/CISS.2015.7086426}, keywords = {Coupled Oscillators; Synchronization}, month = {03}, title = {Synchronization of heterogeneous Kuramoto oscillators with graphs of diameter two}, url = {https://mallada.ece.jhu.edu/pubs/2015-CISS-GMT.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7086426}, year = {2015} }`

- C. Zhao, E. Mallada, and S. H. Low, “Distributed generator and load-side secondary frequency control in power networks,” in Conference on Information Sciences and Systems, 2015. doi:10.1109/CISS.2015.7086825

[BibTeX] [Abstract] [Download PDF]We design distributed secondary frequency control scheme for both generators and controllable loads. The proposed scheme operates via local sensing and computation, and communication between neighbors. Equilibrium and stability analysis of the closed-loop system is performed with a power network model that includes turbines and governors of generators and nonlinear AC power flows. After an unexpected change in power supply or demand, the proposed control is able to stabilize the system, restore bus frequencies and net inter-area power exchanges, and minimize total generation cost minus user utility at equilibrium.

`@inproceedings{zml2015ciss, abstract = {We design distributed secondary frequency control scheme for both generators and controllable loads. The proposed scheme operates via local sensing and computation, and communication between neighbors. Equilibrium and stability analysis of the closed-loop system is performed with a power network model that includes turbines and governors of generators and nonlinear AC power flows. After an unexpected change in power supply or demand, the proposed control is able to stabilize the system, restore bus frequencies and net inter-area power exchanges, and minimize total generation cost minus user utility at equilibrium.}, author = {Zhao, Changhong and Mallada, Enrique and Low, Steven H}, booktitle = {Conference on Information Sciences and Systems}, doi = {10.1109/CISS.2015.7086825}, keywords = {Power Networks; Synchronization}, month = {03}, title = {Distributed generator and load-side secondary frequency control in power networks}, url = {https://mallada.ece.jhu.edu/pubs/2015-CISS-ZML.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7086825}, year = {2015} }`

- A. Gushchin, E. Mallada, and A. Tang, “Synchronization of phase-coupled oscillators with plastic coupling strength,” in Information Theory and Applications Workshop (ITA), 2015, pp. 291-300. doi:10.1109/ITA.2015.7309003

[BibTeX] [Abstract] [Download PDF]In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that, under mild assumptions, such systems are gradient systems, and always achieve frequency synchronization. Furthermore, we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion (necessary and sufficient condition) of stability of equilibria. For both, tree and arbitrary topologies, we provide sufficient conditions for phase-locking, i.e. convergence to a stable equilibrium almost surely. We additionally find conditions when the system possesses a unique stable equilibrium, and thus, almost global stability follows. Several examples are used to demonstrate variety of equilibria the system has, their dependence on system’s parameters, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.

`@inproceedings{gmt2015ita, abstract = {In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that, under mild assumptions, such systems are gradient systems, and always achieve frequency synchronization. Furthermore, we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion (necessary and sufficient condition) of stability of equilibria. For both, tree and arbitrary topologies, we provide sufficient conditions for phase-locking, i.e. convergence to a stable equilibrium almost surely. We additionally find conditions when the system possesses a unique stable equilibrium, and thus, almost global stability follows. Several examples are used to demonstrate variety of equilibria the system has, their dependence on system's parameters, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.}, author = {Gushchin, Andrey and Mallada, Enrique and Tang, Ao}, booktitle = {Information Theory and Applications Workshop (ITA)}, doi = {10.1109/ITA.2015.7309003}, keywords = {Synchronization}, month = {02}, pages = {291-300}, title = {Synchronization of phase-coupled oscillators with plastic coupling strength}, url = {https://mallada.ece.jhu.edu/pubs/2015-ITA-GMT.pdf}, year = {2015} }`

- E. Mallada, C. Zhao, and S. H. Low, “Optimal load-side control for frequency regulation in smart grids,” in 52nd Allerton Conference on Communication, Control, and Computing, 2014, p. 731—738. doi:10.1109/ALLERTON.2014.7028527

[BibTeX] [Abstract] [Download PDF]Frequency control rebalances supply and demand while maintaining the network state within operational margins. It is implemented using fast ramping reserves that are expensive and non-renewable, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints. In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. Our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike generation-side), fair among participating loads, and can further maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and illustrate its convergence with simulation.

`@inproceedings{mzl2014allerton, abstract = {Frequency control rebalances supply and demand while maintaining the network state within operational margins. It is implemented using fast ramping reserves that are expensive and non-renewable, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints. In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. Our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike generation-side), fair among participating loads, and can further maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and illustrate its convergence with simulation.}, author = {Mallada, Enrique and Zhao, Changhong and Low, Steven H}, booktitle = {52nd Allerton Conference on Communication, Control, and Computing}, doi = {10.1109/ALLERTON.2014.7028527}, keywords = {Power Networks}, month = {10}, pages = {731---738}, title = {Optimal load-side control for frequency regulation in smart grids}, url = {https://mallada.ece.jhu.edu/pubs/2014-Allerton-MZL.pdf}, web = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=7028527}, year = {2014} }`

- E. Mallada and S. H. Low, “Distributed frequency-preserving optimal load control,” in IFAC World Congress, 2014, pp. 5411-5418. doi:10.3182/20140824-6-ZA-1003.02012

[BibTeX] [Abstract] [Download PDF]Frequency control is traditionally done on the generation side. Recently we have formulated an optimal load control (OLC) problem and derived a load-side primary frequency control as a primal-dual solution to OLC. The load-side control rebalances power and resynchronize frequencies after a disturbance but cannot restore the nominal frequency. In this paper we modify OLC and derive from it a frequency-preserving load-side control that rebalances power and restores the nominal frequency after a disturbance. Unlike the generation-side secondary frequency control that is centralized, our load-side control only requires each bus to communicate a Lagrange multiplier with its neighbors. We prove that such a distributed load-side control is globally asymptotically stable and illustrate its convergence with simulation.

`@inproceedings{ml2014ifac-wc, abstract = {Frequency control is traditionally done on the generation side. Recently we have formulated an optimal load control (OLC) problem and derived a load-side primary frequency control as a primal-dual solution to OLC. The load-side control rebalances power and resynchronize frequencies after a disturbance but cannot restore the nominal frequency. In this paper we modify OLC and derive from it a frequency-preserving load-side control that rebalances power and restores the nominal frequency after a disturbance. Unlike the generation-side secondary frequency control that is centralized, our load-side control only requires each bus to communicate a Lagrange multiplier with its neighbors. We prove that such a distributed load-side control is globally asymptotically stable and illustrate its convergence with simulation.}, author = {Mallada, Enrique and Low, Steven H}, booktitle = {IFAC World Congress}, doi = {10.3182/20140824-6-ZA-1003.02012}, keywords = {Power Networks; Optimization}, month = {08}, pages = {5411--5418}, title = {Distributed frequency-preserving optimal load control}, url = {https://mallada.ece.jhu.edu/pubs/2014-IFAC-WC-ML.pdf}, year = {2014} }`

- E. Mallada and A. Tang, “Dynamics-aware optimal power flow,” in 52nd IEEE Conference on Decision and Control (CDC), 2013. doi:10.1109/CDC.2013.6760118

[BibTeX] [Abstract] [Download PDF]The development of open electricity markets has led to a decoupling between the market clearing procedure that defines the power dispatch and the security analysis that enforces predefined stability margins. This gap results in market inefficiencies introduced by corrections to the market solution to accommodate stability requirements. In this paper we present an optimal power flow formulation that aims to close this gap. First, we show that the pseudospectral abscissa can be used as a unifying stability measure to characterize both poorly damped oscillations and voltage stability margins. This leads to two novel optimization problems that can find operation points which minimize oscillations or maximize voltage stability margins, and make apparent the implicit tradeoff between these two stability requirements. Finally, we combine these optimization problems to generate a dynamics-aware optimal power flow formulation that provides voltage as well as small signal stability guarantees.

`@inproceedings{mt2013cdc, abstract = {The development of open electricity markets has led to a decoupling between the market clearing procedure that defines the power dispatch and the security analysis that enforces predefined stability margins. This gap results in market inefficiencies introduced by corrections to the market solution to accommodate stability requirements. In this paper we present an optimal power flow formulation that aims to close this gap. First, we show that the pseudospectral abscissa can be used as a unifying stability measure to characterize both poorly damped oscillations and voltage stability margins. This leads to two novel optimization problems that can find operation points which minimize oscillations or maximize voltage stability margins, and make apparent the implicit tradeoff between these two stability requirements. Finally, we combine these optimization problems to generate a dynamics-aware optimal power flow formulation that provides voltage as well as small signal stability guarantees.}, author = {Mallada, Enrique and Tang, Ao}, booktitle = {52nd IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2013.6760118}, keywords = {Power Networks; Optimization}, month = {12}, title = {Dynamics-aware optimal power flow}, url = {https://mallada.ece.jhu.edu/pubs/2013-CDC-MT.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6760118}, year = {2013} }`

- E. Mallada, X. Meng, M. Hack, L. Zhang, and A. Tang, “Skewless network clock synchronization,” in 21st IEEE International Conference on Network Protocols (ICNP), 2013, pp. 1-10. doi:10.1109/ICNP.2013.6733612

[BibTeX] [Abstract] [Download PDF]This paper examines synchronization of computer clocks connected via a data network and proposes a skewless algorithm to synchronize them. Unlike existing solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, our algorithm achieves synchronization without these problems. We first analyze the convergence property of the algorithm and provide necessary and sufficient conditions on the parameters to guarantee synchronization. We then implement our solution on a cluster of IBM BladeCenter servers running Linux and study its performance. In particular, both analytically and experimentally, we show that our algorithm can converge in the presence of timing loops. This marks a clear contrast with current standards such as NTP and PTP, where timing loops are specifically avoided. Furthermore, timing loops can even be beneficial in our scheme. For example, it is demonstrated that highly connected subnetworks can collectively outperform individual clients when the time source has large jitter. It is also experimentally demonstrated that our algorithm outperforms other well-established software-based solutions such as the NTPv4 and IBM Coordinated Cluster Time (IBM CCT).

`@inproceedings{mmhzt2013icnp, abstract = {This paper examines synchronization of computer clocks connected via a data network and proposes a skewless algorithm to synchronize them. Unlike existing solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, our algorithm achieves synchronization without these problems. We first analyze the convergence property of the algorithm and provide necessary and sufficient conditions on the parameters to guarantee synchronization. We then implement our solution on a cluster of IBM BladeCenter servers running Linux and study its performance. In particular, both analytically and experimentally, we show that our algorithm can converge in the presence of timing loops. This marks a clear contrast with current standards such as NTP and PTP, where timing loops are specifically avoided. Furthermore, timing loops can even be beneficial in our scheme. For example, it is demonstrated that highly connected subnetworks can collectively outperform individual clients when the time source has large jitter. It is also experimentally demonstrated that our algorithm outperforms other well-established software-based solutions such as the NTPv4 and IBM Coordinated Cluster Time (IBM CCT).}, author = {Mallada, Enrique and Meng, Xiaoqiao and Hack, Michel and Zhang, Li and Tang, Ao}, booktitle = {21st IEEE International Conference on Network Protocols (ICNP)}, doi = {10.1109/ICNP.2013.6733612}, keywords = {Networking; Synchronization}, month = {10}, pages = {1--10}, title = {Skewless network clock synchronization}, url = {https://mallada.ece.jhu.edu/pubs/2013-ICNP-MMHZT.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6733612}, year = {2013} }`

- M. Wang, W. Xu, E. Mallada, and A. Tang, “Sparse recovery with graph constraints: Fundamental limits and measurement construction,” in Proceedings of IEEE Infocom, 2012, pp. 1871-1879. doi:10.1109/INFCOM.2012.6195562

[BibTeX] [Abstract] [Download PDF]This paper addresses the problem of sparse recovery with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs. A general measurement construction algorithm is also proposed and evaluated. For any given graph G with n nodes, we derive order optimal upper bounds of the minimum number of measurements needed to recover any k-sparse vector over $G (M_k,n^G)$. Our study suggests that $M_k,n^G$ may serve as a graph connectivity metric.

`@inproceedings{wxmt2012infocom, abstract = {This paper addresses the problem of sparse recovery with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs. A general measurement construction algorithm is also proposed and evaluated. For any given graph G with n nodes, we derive order optimal upper bounds of the minimum number of measurements needed to recover any k-sparse vector over $G (M_k,n^G)$. Our study suggests that $M_k,n^G$ may serve as a graph connectivity metric.}, author = {Wang, Meng and Xu, Weiyu and Mallada, Enrique and Tang, Ao}, booktitle = {Proceedings of IEEE Infocom}, doi = {10.1109/INFCOM.2012.6195562}, keywords = {Sparse Recovery}, month = {03}, pages = {1871--1879}, title = {Sparse recovery with graph constraints: Fundamental limits and measurement construction}, url = {https://mallada.ece.jhu.edu/pubs/2012-Infocom-WXMT.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6195562}, year = {2012} }`

- E. Mallada and A. Tang, “Improving damping of power networks: Power scheduling and impedance adaptation,” in 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011, pp. 7729-7734. doi:10.1109/CDC.2011.6161287

[BibTeX] [Abstract] [Download PDF]This paper studies the effect of power scheduling and line impedances on the damping of a power network. We relate the damping of a network with the algebraic connectivity of a state dependent Laplacian. Via implicit function theorem, we further characterize its dependence on network parameters. This allows us to derive several updating directions that can locally improve the damping. The analysis also provides some interesting insight. For example, improving connectivity, by adding lines for instance, may not be beneficial in terms of damping.

`@inproceedings{mt2011cdcb, abstract = {This paper studies the effect of power scheduling and line impedances on the damping of a power network. We relate the damping of a network with the algebraic connectivity of a state dependent Laplacian. Via implicit function theorem, we further characterize its dependence on network parameters. This allows us to derive several updating directions that can locally improve the damping. The analysis also provides some interesting insight. For example, improving connectivity, by adding lines for instance, may not be beneficial in terms of damping.}, author = {Mallada, Enrique and Tang, Ao}, booktitle = {50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)}, doi = {10.1109/CDC.2011.6161287}, keywords = {Power Networks; Optimization}, month = {12}, pages = {7729--7734}, title = {Improving damping of power networks: Power scheduling and impedance adaptation}, url = {https://mallada.ece.jhu.edu/pubs/2011-CDCb-MT.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6161287}, year = {2011} }`

- E. Mallada and A. Tang, “Distributed clock synchronization: Joint frequency and phase consensus,” in 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011, pp. 6742-6747. doi:10.1109/CDC.2011.6161231

[BibTeX] [Abstract] [Download PDF]Distributed synchronization has gradually gained importance over the last two decades. The ad-hoc nature of new applications has increased the need for robust and scalable distributed algorithms that are capable of generating high precision timing information. However, current solutions usually produce phase errors when the frequencies are heterogeneous. This paper proposes a distributed synchronization procedure that can achieve consensus in both frequency and phase. The algorithm uses only local information and is robust to frequency heterogeneity and network topology. A sufficient condition for global convergence is shown by leveraging recent results on coupled oscillators. We further characterize an invariant constant of the algorithm that relates the limiting frequency $ømega^*$ with the harmonic mean of the clocks’ natural frequencies. Simulations are provided to illustrate and verify these properties.

`@inproceedings{mt2011cdca, abstract = {Distributed synchronization has gradually gained importance over the last two decades. The ad-hoc nature of new applications has increased the need for robust and scalable distributed algorithms that are capable of generating high precision timing information. However, current solutions usually produce phase errors when the frequencies are heterogeneous. This paper proposes a distributed synchronization procedure that can achieve consensus in both frequency and phase. The algorithm uses only local information and is robust to frequency heterogeneity and network topology. A sufficient condition for global convergence is shown by leveraging recent results on coupled oscillators. We further characterize an invariant constant of the algorithm that relates the limiting frequency $ømega^*$ with the harmonic mean of the clocks' natural frequencies. Simulations are provided to illustrate and verify these properties.}, author = {Mallada, Enrique and Tang, Ao}, booktitle = {50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)}, doi = {10.1109/CDC.2011.6161231}, keywords = {Coupled Oscillators; Synchronization}, month = {12}, pages = {6742--6747}, title = {Distributed clock synchronization: Joint frequency and phase consensus}, url = {https://mallada.ece.jhu.edu/pubs/2011-CDCa-MT.pdf}, web = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6161231}, year = {2011} }`

- W. Xu, M. Wang, E. Mallada, and A. Tang, “Recent results on sparse recovery over graphs,” in Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 2011, pp. 413-417. doi:10.1109/ACSSC.2011.6190031

[BibTeX] [Abstract] [Download PDF]In this paper, we review our recent results on sparse recovery over graphs, which was motivated by network tomography problems. Our finding has made a new connection between coding theory and graph theory. We also discuss robustness of our proposed measurement construction.

`@inproceedings{xwmt2011asilomar, abstract = {In this paper, we review our recent results on sparse recovery over graphs, which was motivated by network tomography problems. Our finding has made a new connection between coding theory and graph theory. We also discuss robustness of our proposed measurement construction.}, author = {Xu, Weiyu and Wang, Meng and Mallada, Enrique and Tang, Ao}, booktitle = {Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)}, doi = {10.1109/ACSSC.2011.6190031}, keywords = {Sparse Recovery}, month = {11}, pages = {413--417}, title = {Recent results on sparse recovery over graphs}, url = {https://mallada.ece.jhu.edu/pubs/2011-Asilomar-XWMT.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6190031}, year = {2011} }`

- W. Xu, E. Mallada, and A. Tang, “Compressive sensing over graphs,” in Proceeding of IEEE Infocom, 2011, pp. 2087-2095. doi:10.1109/INFCOM.2011.5935018

[BibTeX] [Abstract] [Download PDF]In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the properties of the edges from a graph. Unlike existing compressive sensing results, the collective additive measurements we are allowed to take must follow connected paths over the underlying graph. For a sufficiently connected graph with n nodes, it is shown that, using O(k log(n)) path measurements, we are able to recover any k-sparse link vector (with no more than k nonzero elements), even though the measurements have to follow the graph path constraints. We mainly show that the computationally efficient ℓ1 minimization can provide theoretical guarantees for inferring such k-sparse vectors with O(k log(n)) path measurements from the graph.

`@inproceedings{xmt2011infocom, abstract = {In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the properties of the edges from a graph. Unlike existing compressive sensing results, the collective additive measurements we are allowed to take must follow connected paths over the underlying graph. For a sufficiently connected graph with n nodes, it is shown that, using O(k log(n)) path measurements, we are able to recover any k-sparse link vector (with no more than k nonzero elements), even though the measurements have to follow the graph path constraints. We mainly show that the computationally efficient ℓ1 minimization can provide theoretical guarantees for inferring such k-sparse vectors with O(k log(n)) path measurements from the graph.}, author = {Xu, Weiyu and Mallada, Enrique and Tang, Ao}, booktitle = {Proceeding of IEEE Infocom}, doi = {10.1109/INFCOM.2011.5935018}, keywords = {Sparse Recovery}, month = {03}, organization = {IEEE}, pages = {2087--2095}, title = {Compressive sensing over graphs}, url = {https://mallada.ece.jhu.edu/pubs/2011-Infocom-XMT.pdf}, year = {2011} }`

- E. Mallada and A. Tang, “Weakly pulse-coupled oscillators: Heterogeneous delays lead to homogeneous phase,” in 49th IEEE Conference on Decision and Control (CDC), 2010, pp. 992-997. doi:10.1109/CDC.2010.5717864

[BibTeX] [Abstract] [Download PDF]This paper studies the effect of heterogeneous delays in networks of weakly pulse-coupled identical oscillators. We develop a new framework to study them by constructing a non-delayed phase model that is equivalent to the original one in the continuum limit. Using existing results for non-delayed phase-coupled oscillators we analyze the delayed system and show how its stability properties depend on the delay distribution. In particular, we show that in some scenarios, heterogeneity, i.e. wider delay distribution, can help reach in-phase synchronization.

`@inproceedings{mt2010cdc, abstract = {This paper studies the effect of heterogeneous delays in networks of weakly pulse-coupled identical oscillators. We develop a new framework to study them by constructing a non-delayed phase model that is equivalent to the original one in the continuum limit. Using existing results for non-delayed phase-coupled oscillators we analyze the delayed system and show how its stability properties depend on the delay distribution. In particular, we show that in some scenarios, heterogeneity, i.e. wider delay distribution, can help reach in-phase synchronization.}, author = {Mallada, Enrique and Tang, Ao}, booktitle = {49th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2010.5717864}, keywords = {Coupled Oscillators; Synchronization}, month = {12}, pages = {992--997}, title = {Weakly pulse-coupled oscillators: Heterogeneous delays lead to homogeneous phase}, url = {https://mallada.ece.jhu.edu/pubs/2010-CDC-MT.pdf}, web = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=5717864}, year = {2010} }`

- E. Mallada and A. Tang, “Synchronization of phase-coupled oscillators with arbitrary topology,” in 2010 American Control Conference (ACC), 2010, pp. 1777-1782. doi:10.1109/ACC.2010.5531468

[BibTeX] [Abstract] [Download PDF]This paper studies networks of identical phase-coupled oscillators with arbitrary underlying connected graph. By using results from algebraic graph theory, a sufficient condition is obtained which can be used to check equilibrium stability. This condition generalizes existing results and can solve some previously unsolved cases. It also leads to the first sufficient condition on the coupling function with which the system is guaranteed to reach synchronization. Throughout the paper, several examples are used to verify and illustrate the theory. We also correct some mistakes in the existing literature.

`@inproceedings{mt2010acc, abstract = {This paper studies networks of identical phase-coupled oscillators with arbitrary underlying connected graph. By using results from algebraic graph theory, a sufficient condition is obtained which can be used to check equilibrium stability. This condition generalizes existing results and can solve some previously unsolved cases. It also leads to the first sufficient condition on the coupling function with which the system is guaranteed to reach synchronization. Throughout the paper, several examples are used to verify and illustrate the theory. We also correct some mistakes in the existing literature.}, author = {Mallada, Enrique and Tang, Ao}, booktitle = {2010 American Control Conference (ACC)}, doi = {10.1109/ACC.2010.5531468}, keywords = {Coupled Oscillators; Synchronization}, month = {06}, pages = {1777--1782}, title = {Synchronization of phase-coupled oscillators with arbitrary topology}, url = {https://mallada.ece.jhu.edu/pubs/2010-ACC-MT.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5531468}, year = {2010} }`

- E. Mallada and F. Paganini, “Stability of node-based multipath routing and dual congestion control,” in 47th IEEE Conference on Decision and Control (CDC), 2008, pp. 1398-1403. doi:10.1109/CDC.2008.4739209

[BibTeX] [Abstract] [Download PDF]This paper considers a network flow control problem where routing and input rates are controlled in a decentralized way across a network, to optimize a global welfare objective. We build on our recent work which combines “dual” congestion control for the traffic sources, with multipath routing at the router nodes, controlling the traffic split among outgoing links based on downstream congestion prices. The challenge is to obtain stabilization of the optimum point; in fact, controlling the split fractions following the price gradient has the correct equilibrium, but can lead to oscillatory instabilities. This suggests the use of derivative action to damp such oscillations. We study two alternatives in this regard; either anticipatory control of routing splits, which yields local stability in an arbitrary network topology, or anticipatory price generation, which yields a global result for the case of a network of parallel links. Proofs are based on a Lyapunov argument. Results are illustrated through simulations.

`@inproceedings{mp2008cdc, abstract = {This paper considers a network flow control problem where routing and input rates are controlled in a decentralized way across a network, to optimize a global welfare objective. We build on our recent work which combines ``dual'' congestion control for the traffic sources, with multipath routing at the router nodes, controlling the traffic split among outgoing links based on downstream congestion prices. The challenge is to obtain stabilization of the optimum point; in fact, controlling the split fractions following the price gradient has the correct equilibrium, but can lead to oscillatory instabilities. This suggests the use of derivative action to damp such oscillations. We study two alternatives in this regard; either anticipatory control of routing splits, which yields local stability in an arbitrary network topology, or anticipatory price generation, which yields a global result for the case of a network of parallel links. Proofs are based on a Lyapunov argument. Results are illustrated through simulations.}, author = {Mallada, Enrique and Paganini, Fernando}, booktitle = {47th IEEE Conference on Decision and Control (CDC)}, doi = {10.1109/CDC.2008.4739209}, keywords = {Networking}, month = {12}, pages = {1398--1403}, title = {Stability of node-based multipath routing and dual congestion control}, url = {https://mallada.ece.jhu.edu/pubs/2008-CDC-MP.pdf}, web = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4739209&tag=1}, year = {2008} }`

- E. Mallada and F. Paganini, “Optimal congestion control with multipath routing using TCP-FAST and a variant of RIP,” in NET-COOP, 2007, pp. 205-214. doi:10.1007/978-3-540-72709-5_22

[BibTeX] [Abstract] [Download PDF]This paper discusses an optimization-based approach for congestion control together with multipath routing in a TCP/IP network. In recent research we have shown how natural optimization problems for resource allocation can be solved in decentralized way across a network, by traffic sources adapting their rates and routers adapting their traffic splits, all using a common congestion measure. We present here a concrete implementation of such algorithms, based on queueing delay as congestion price. We use TCP-FAST for congestion control, and develop a multipath variant of the distance vector routing protocol RIP. We demonstrate through ns2-simulations the collective behavior of the system, in particular that it reaches the higher transfer rates available through multiple routes.

`@inproceedings{mp2007netcoop, abstract = {This paper discusses an optimization-based approach for congestion control together with multipath routing in a TCP/IP network. In recent research we have shown how natural optimization problems for resource allocation can be solved in decentralized way across a network, by traffic sources adapting their rates and routers adapting their traffic splits, all using a common congestion measure. We present here a concrete implementation of such algorithms, based on queueing delay as congestion price. We use TCP-FAST for congestion control, and develop a multipath variant of the distance vector routing protocol RIP. We demonstrate through ns2-simulations the collective behavior of the system, in particular that it reaches the higher transfer rates available through multiple routes.}, author = {Mallada, Enrique and Paganini, Fernando}, booktitle = {NET-COOP}, doi = {10.1007/978-3-540-72709-5_22}, keywords = {Networking}, month = {06}, note = {also in Lecture Notes in Computer Science 4465, Springer-Verlag, Berlin-Heidelberg}, pages = {205--214}, title = {Optimal congestion control with multipath routing using TCP-FAST and a variant of RIP}, url = {https://mallada.ece.jhu.edu/pubs/2007-NETCOOP-MP.pdf}, year = {2007} }`

- F. Paganini and E. Mallada, “Congestion pricing for flow control and multipath routing in TCP/IP networks,” in Congreso Latinoamericano de Investigación Operativa, 2006.

[BibTeX] [Abstract] [Download PDF]We consider a TCP/IP style network, in which end-systems control their traffic rates based on congestion feedback, and routing is performed at intermediate nodes on a perdestination basis; extending standard IP, routers are allowed to use multiple outgoing links per destination. We pose two optimization problems, that generalize and combine those in congestion control and traffic engineering, with variables which are local to either sources or routers. We obtain decentralized algorithms by propagating price variables and using them to control source rates and router traffic splits; we give conditions for convergence of these algorithms to optimal points. Keywords: congestion control, routing, TCP/IP, optimization, pricing.

`@inproceedings{pm2006claio, abstract = {We consider a TCP/IP style network, in which end-systems control their traffic rates based on congestion feedback, and routing is performed at intermediate nodes on a perdestination basis; extending standard IP, routers are allowed to use multiple outgoing links per destination. We pose two optimization problems, that generalize and combine those in congestion control and traffic engineering, with variables which are local to either sources or routers. We obtain decentralized algorithms by propagating price variables and using them to control source rates and router traffic splits; we give conditions for convergence of these algorithms to optimal points. Keywords: congestion control, routing, TCP/IP, optimization, pricing.}, author = {Paganini, Fernando and Mallada, Enrique}, booktitle = {Congreso Latinoamericano de Investigación Operativa}, keywords = {Networking}, month = {11}, title = {Congestion pricing for flow control and multipath routing in TCP/IP networks}, url = {https://mallada.ece.jhu.edu/pubs/2006-CLAIO-MP.pdf}, year = {2006} }`

**Abstracts**

- C. Ji, M. H. Hajiesmaili, D. F. Gayme, and E. Mallada, Coordinating Distribution System Resources for Co-optimized Participation in Energy and Ancillary Service Transmission System Markets, 2018.

[BibTeX] [Download PDF]`@misc{jhgm2018ferc-taic, author = {Ji, Chengda and Hajiesmaili, Mohammad H. and Gayme, Dennice F. and Mallada, Enrique}, grants = {CAREER-1752362, ENERGISE-DE-EE0008006, EPCN-1711188}, howpublished = {FERC Trans-Atlantic Infraday Workshop}, month = {11}, title = {Coordinating Distribution System Resources for Co-optimized Participation in Energy and Ancillary Service Transmission System Markets}, url = {https://mallada.ece.jhu.edu/pubs/2018-FERC-TAIC-JHGM.pdf}, year = {2018} }`

**Theses**

- E. Mallada, “Distributed synchronization in engineering networks: The Internet and electric power girds,” PhD Thesis, 2014.

[BibTeX] [Abstract] [Download PDF]Synchronization is a fundamental requirement of most networked engineering applications. It enables the necessary coordination among agents required to implement several communication systems as well as network protocols. Despite the great recent advances in understanding synchronization, a complete synchronization theory is yet to be developed. This thesis presents a systematic study of synchronization on distributed systems that covers theoretical guarantees for synchronization, performance analysis and optimization, as well as design and implementation of algorithms. We first present several theoretical results that deepen the understanding of how coupling, delay and topology affect the behavior of a system of coupled oscillators. We obtain a sufficient condition that can be used to check limit cycle stability, and use it to characterize a family of coupling functions guaranteeing convergence to in-phase synchronization (phase consensus). The effect of heterogeneous delay is then investigated by developing a new framework that unveils the dependence of the orbit’s stability on the delay distribution. Finally, we consider the effect of frequency heterogeneity. While coupled oscillators with heterogeneous frequency cannot achieve phase consensus, we show that a second order version of the system can achieve synchronization for arbitrary natural frequencies and we relate the limiting frequency of the system to the harmonic mean of the natural frequencies. Based on the insight provided by our theoretical results, we then focus on more practical aspects of synchronization in two particular areas: information networks and power networks. Within information networks, we examine the synchronization of computer clocks connected via a data network and propose a discrete algorithm to synchronize them. Unlike current solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, this algorithm achieves synchronization without any of these problems. We present a detailed convergence analysis together with a characterization of the parameter values that guarantee convergence. We then study and optimize the effect of noisy measurements and clock wander on the system performance using a parameter dependent H2 norm. In particular, we show that the frequency of the system drifts away from its theoretical value in the absence of a leader. We implement the algorithm on a cluster of IBM BladeCenter servers running Linux and we experimentally verify that our algorithm outperforms the well-established solution. We also show that the optimal parameter values depend on the network conditions and topology. Finally, we study synchronization on power networks. By relating the dynamics of power networks to the dynamics of coupled oscillators, we can gain insight into how different network parameters affect performance. We show that the rate of convergence of networks is related to the algebraic connectivity of a state dependent Laplacian which varies with the network power scheduling and line impedances. This provides a novel method to change the voltage stability margins by updating the power scheduling or line impedances. Unfortunately, there exists a decoupling between the market clearing procedure used to dispatch power and the security analysis of the network, that prevents the direct use of this solution. Furthermore, focusing on voltage stability may generate other types of instabilities such as larger transient oscillations. This motivates the use of a unifying stability measure that can minimize oscillations or maximize voltage stability margins, and can be readily combined with current dispatch mechanisms generating a dynamics-aware optimal power flow formulation.

`@phdthesis{m2014phd-thesis, abstract = {Synchronization is a fundamental requirement of most networked engineering applications. It enables the necessary coordination among agents required to implement several communication systems as well as network protocols. Despite the great recent advances in understanding synchronization, a complete synchronization theory is yet to be developed. This thesis presents a systematic study of synchronization on distributed systems that covers theoretical guarantees for synchronization, performance analysis and optimization, as well as design and implementation of algorithms. We first present several theoretical results that deepen the understanding of how coupling, delay and topology affect the behavior of a system of coupled oscillators. We obtain a sufficient condition that can be used to check limit cycle stability, and use it to characterize a family of coupling functions guaranteeing convergence to in-phase synchronization (phase consensus). The effect of heterogeneous delay is then investigated by developing a new framework that unveils the dependence of the orbit's stability on the delay distribution. Finally, we consider the effect of frequency heterogeneity. While coupled oscillators with heterogeneous frequency cannot achieve phase consensus, we show that a second order version of the system can achieve synchronization for arbitrary natural frequencies and we relate the limiting frequency of the system to the harmonic mean of the natural frequencies. Based on the insight provided by our theoretical results, we then focus on more practical aspects of synchronization in two particular areas: information networks and power networks. Within information networks, we examine the synchronization of computer clocks connected via a data network and propose a discrete algorithm to synchronize them. Unlike current solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, this algorithm achieves synchronization without any of these problems. We present a detailed convergence analysis together with a characterization of the parameter values that guarantee convergence. We then study and optimize the effect of noisy measurements and clock wander on the system performance using a parameter dependent H2 norm. In particular, we show that the frequency of the system drifts away from its theoretical value in the absence of a leader. We implement the algorithm on a cluster of IBM BladeCenter servers running Linux and we experimentally verify that our algorithm outperforms the well-established solution. We also show that the optimal parameter values depend on the network conditions and topology. Finally, we study synchronization on power networks. By relating the dynamics of power networks to the dynamics of coupled oscillators, we can gain insight into how different network parameters affect performance. We show that the rate of convergence of networks is related to the algebraic connectivity of a state dependent Laplacian which varies with the network power scheduling and line impedances. This provides a novel method to change the voltage stability margins by updating the power scheduling or line impedances. Unfortunately, there exists a decoupling between the market clearing procedure used to dispatch power and the security analysis of the network, that prevents the direct use of this solution. Furthermore, focusing on voltage stability may generate other types of instabilities such as larger transient oscillations. This motivates the use of a unifying stability measure that can minimize oscillations or maximize voltage stability margins, and can be readily combined with current dispatch mechanisms generating a dynamics-aware optimal power flow formulation.}, author = {Mallada, Enrique}, keywords = {Coupled Oscillators; Networking; Power Networks; Synchronization}, month = {01}, school = {Electrical and Computer Engineering, Cornell University}, title = {Distributed synchronization in engineering networks: The Internet and electric power girds}, url = {https://mallada.ece.jhu.edu/pubs/2014-Thesis-M.pdf}, web = {http://ecommons.library.cornell.edu/handle/1813/36073}, year = {2014} }`