Online Feedback Equilibrium Seeking

Giuseppe Belgioioso*, Dominic Liao-McPherson*, Mathias Hudoba de Badyn, Saverio Bolognani, Roy S. Smith, John Lygeros, and Florian Dörfler

IEEE Transactions on Automatic Control

arXiv:2210.12088 [math.OC]

This paper proposes a unifying design framework for dynamic feedback controllers that track solution trajectories of time-varying generalized equations, such as local minimizers of nonlinear programs or competitive equilibria (e.g., Nash) of non-cooperative games. Inspired by the feedback optimization paradigm, the core idea of the proposed approach is to re-purpose classic iterative algorithms for solving generalized equations (e.g., Josephy-Newton, forward-backward splitting) as feedback controllers by integrating online measurements of the continuous-time nonlinear physical plant. Sufficient conditions for closed-loop stability and robustness of the algorithm-plant cyber-physical interconnection are derived in a sampled-data setting by combining and tailoring results from (monotone) operator, fixed-point, and nonlinear systems theory. Numerical simulations on smart building automation and competitive supply-chain management are presented to support the theoretical findings.

Applications

Smart buildings

Section VII.A in

Online Feedback Equilibrium Seeking
Giuseppe Belgioioso*, Dominic Liao-McPherson*, Mathias Hudoba de Badyn, Saverio Bolognani, Roy S. Smith, John Lygeros, and Florian Dörfler
arXiv:2210.12088 [math.OC]

Supply chains

Section VII.B in

Power grids

Tutorial on Congestion Control in Multi-Area Transmission Grids via Online Feedback Equilibrium Seeking
Giuseppe Belgioioso, Saverio Bolognani, Giulia Pejrani, Florian Dörfler
IEEE Conference on Decision and Control, 2023

Slides

Conference papers and talks

Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking
Giuseppe Belgioioso, Dominic Liao-McPherson, Mathias Hudoba de Badyn, Saverio Bolognani, John Lygeros, Florian Dörfler
IEEE Conference on Decision and Control, 2021
10.1109/CDC45484.2021.9683614 - Preprint on arXiv:2103.13988 [math.OC]

Related works

A non-exhaustive list of papers that are related to our feedback equilibrium seeking research and that are worth a read.

Optimization Algorithms as Robust Feedback Controllers
Adrian Hauswirth, Zhiyu He, Saverio Bolognani, Gabriela Hug, Florian Dörfler
arXiv:2103.11329 [math.OC], 2021
10.48550/arXiv.2103.11329

Game-Theoretic Feedback-Based Optimization
Anurag Agarwal, John W. Simpson-Porco, Lacra Pavel
9th IFAC Conference on Networked Systems (NECSYS), 2022
10.1016/j.ifacol.2022.07.255

Model-Free Game-Theoretic Feedback Optimization
Anurag Agarwal, John W. Simpson-Porco, Lacra Pavel
European Control Conference (ECC), 2023
10.23919/ECC57647.2023.10178314

Perception-Based Sampled-Data Optimization of Dynamical Systems
Liliaokeawawa Cothren, Gianluca Bianchin, Sarah Dean, Emiliano Dall'Anese
22nd IFAC World Congress, 2023
10.1016/j.ifacol.2023.10.1290

A Framework for a Class of Hybrid Extremum Seeking Controllers with Dynamic Inclusions
Jorge I. Poveda, Andrew R. Teel
Automatica, Volume 76, 2017
10.1016/j.automatica.2016.10.029

Contracting Dynamics for Time-Varying Convex Optimization
Alexander Davydov, Veronica Centorrino, Anand Gokhale, Giovanni Russo, Francesco Bullo
arXiv:2305.15595 [math.OC], 2023
10.48550/arXiv.2305.15595