Online Feedback Equilibrium Seeking
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Publication:6506853
arXiv2210.12088MaRDI QIDQ6506853
John Lygeros, Giuseppe Belgioioso, Saverio Bolognani, Dominic Liao-McPherson, Mathias Hudoba de Badyn, Roy S. Smith, Florian Dörfler
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 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.
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