Online Feedback Equilibrium Seeking

TL;DR

This paper introduces a unified framework for designing dynamic feedback controllers that track solutions of time-varying generalized equations, ensuring stability and robustness in cyber-physical systems through online measurements.

Contribution

It re-purposes classic iterative algorithms as feedback controllers for nonlinear plants, providing stability conditions and demonstrating applications in smart buildings and supply chains.

Findings

Stable closed-loop control achieved with the proposed framework.

Robustness of the control system under sampled-data conditions.

Successful numerical validation in building automation and supply-chain management.

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.