Online Feedback Equilibrium Seeking
Abstract
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 dynamic feedback controllers by integrating online measurements of the continuous-time nonlinear 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.
Keywords
Cite
@article{arxiv.2210.12088,
title = {Online Feedback Equilibrium Seeking},
author = {Giuseppe Belgioioso and Dominic Liao-McPherson and Mathias Hudoba de Badyn and Saverio Bolognani and Roy S. Smith and John Lygeros and Florian Dörfler},
journal= {arXiv preprint arXiv:2210.12088},
year = {2024}
}