Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking

TL;DR

This paper introduces a unified feedback control framework for driving complex systems to optimal or equilibrium states using sampled-data methods, with proven stability and robustness.

Contribution

It develops a novel closed-loop equilibrium seeking approach that integrates iterative algorithms with physical systems, providing the first stability results for sampled-data feedback optimization.

Findings

Proven stability and robustness conditions for the proposed feedback controllers.

Validated approach through simulations in smart building and robotic swarm scenarios.

Abstract

This paper proposes a general framework for constructing feedback controllers that drive complex dynamical systems to "efficient" steady-state (or slowly varying) operating points. Efficiency is encoded using generalized equations which can model a broad spectrum of useful objectives, such as optimality or equilibria (e.g. Nash, Wardrop, etc.) in noncooperative games. The core idea of the proposed approach is to directly implement iterative solution (or equilibrium seeking) algorithms in closed loop with physical systems. Sufficient conditions for closed-loop stability and robustness are derived; these also serve as the first closed-loop stability results for sampled-data feedback-based optimization. Numerical simulations of smart building automation and game-theoretic robotic swarm coordination support the theoretical results.