Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking

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 sampleddata feedback-based optimization. Numerical simulations of smart building automation and game-theoretic robotic swarm coordination support the theoretical results.

Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis

“…First, we upper bound the right hand side of (10). To this aim, by combining (9) with Assumption 2(a) and by application of Lemma 2.5 we have:…”

“…This paper focuses on the design of output feedback controllers to regulate the inputs and outputs of a discretetime linear time-invariant system to the solution of a convex optimization problem. Our controller synthesis is inspired by principled optimization methods, properly modified to account for output feedback from the dynamical system (similarly to [2]- [9]). These problems are relevant in application domains such as power grids [4], [10], transportation systems [7], robotics [8], and control of epidemics [11], where the target optimization problem encodes desired performance objectives and constraints (possibly dynamic and time-varying) of the system at equilibrium.…”

“…Most of the recent literature on online optimization for dynamical systems critically relies on the assumption that the system dynamics are known [2]- [4], [6], [7], [9], [12]. Unfortunately, perfect system knowledge is rarely available in practice -especially when exogenous disturbances are not observable and/or inputs are not persistently exciting -because maintaining and refining full system model often requires ad-hoc system-identification phases.…”