Our papers on strategic behavior of load participants in two-stage settlement electricity markets [1], model predictive control via second order cone programming [2], and dynamics concentration of tightly-connected networks [3] have been accepted to IEEE Conference on Decision and Control!

[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}
}
```

[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}
}
```

[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}
}
```