# 6 papers accepted to ACC 21

6 papers [1, 2, 3, 4, 5, 6] have been accepted to American Control Conference(ACC) 2021!

[1] J. Guthrie and E. Mallada, “Outer Approximations of Minkowski Operations on Complex Sets via Sum-of-Squares Optimization,” in American Control Conference (ACC), 2021, pp. 2367-2373.

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 (ACC)},
doi = {10.23919/ACC50511.2021.9482940},
grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979},
month = {5},
pages = {2367-2373},
record = {submitted Sep. 2020, accepted Jan. 2021},
title = {Outer Approximations of Minkowski Operations on Complex Sets via Sum-of-Squares Optimization},
year = {2021}
}
[2] P. You and E. Mallada, “Saddle Flow Dynamics: Observable Certificates and Separable Regularization,” in American Control Conference (ACC), 2021, pp. 4817-4823.

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 (ACC)},
doi = {10.23919/ACC50511.2021.9483346},
grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979},
month = {5},
pages = {4817-4823},
record = {submitted Sep. 2020, accepted Jan. 2021},
title = {Saddle Flow Dynamics: Observable Certificates and Separable Regularization},
year = {2021}
}
[3] H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” in American Control Conference (ACC), 2021, pp. 570-575.

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 (ACC)},
doi = {10.23919/ACC50511.2021.9483031},
grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092},
month = {5},
pages = {570-575},
record = {submitted Sep. 2020, accepted Jan. 2021},
title = {Accurate Reduced Order Models for Coherent Heterogeneous Generators},
year = {2021}
}
[4] Y. Jiang, A. Bernstein, P. Vorobev, and E. Mallada, “Grid-forming frequency shaping control in low inertia power systems,” in American Control Conference (ACC), 2021, pp. 4184-4189.

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{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 (ACC)},
doi = {10.23919/ACC50511.2021.9482678},
grants = {CAREER-1752362, AMPS-1736448, TRIPODS-1934979, EPCN-1711188},
month = {5},
pages = {4184-4189},
record = {submitted Sep. 2020, accepted Jan. 2021},
title = {Grid-forming frequency shaping control in low inertia power systems},
year = {2021}
}
[5] A. Castellano, J. Bazerque, and E. Mallada, “Learning to be safe, in finite time,” in American Control Conference (ACC), 2021, pp. 909-916.

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 (ACC)},
doi = {10.23919/ACC50511.2021.9482829},
grants = {CPS-1544771, CAREER-1752362, TRIPODS-1934979},
month = {5},
pages = {909-916},
record = {submitted Sep. 2020, accepted Jan. 2021},
title = {Learning to be safe, in finite time},
year = {2021}
}
[6] R. K. Bansal, P. You, D. F. Gayme, and E. Mallada, “Storage Degradation Aware Economic Dispatch,” in American Control Conference (ACC), 2021, pp. 589-595.

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 (ACC)},
doi = {10.23919/ACC50511.2021.9482838},
grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979},
month = {5},
pages = {589-595},
record = {submitted Sep. 2020, accepted Jan. 2021},
title = {Storage Degradation Aware Economic Dispatch},