Data-driven control of switched linear systems with probabilistic stability guarantees

TL;DR

This paper presents a data-driven control method for switched linear systems that guarantees probabilistic stability without prior knowledge of system dynamics, using finite trajectory data and Lyapunov functions.

Contribution

It introduces a novel framework for stabilizing switched systems with probabilistic guarantees based solely on observed data, without system model knowledge.

Findings

Provides probabilistic stability guarantees for data-driven controllers

Develops scalable parallelized algorithms for high-dimensional systems

Extends quadratic Lyapunov methods to LQR control design

Abstract

This paper tackles state feedback control of switched linear systems under arbitrary switching. We propose a data-driven control framework that allows to compute a stabilizing state feedback using only a finite set of observations of trajectories with quadratic and sum of squares (SOS) Lyapunov functions. We do not require any knowledge on the dynamics or the switching signal, and as a consequence, we aim at solving \emph{uniform} stabilization problems in which the feedback is stabilizing for all possible switching sequences. In order to generalize the solution obtained from trajectories to the actual system, probabilistic guarantees on the obtained quadratic or SOS Lyapunov function are derived in the spirit of scenario optimization. For the quadratic Lyapunov technique, the generalization relies on a geometric analysis argument, while, for the SOS Lyapunov technique, we follow a sensitivity analysis argument. In order to deal with high-dimensional systems, we also develop parallelized schemes for both techniques. We show that, with some modifications, the data-driven quadratic Lyapunov technique can be extended to LQR control design. Finally, the proposed data-driven control framework is demonstrated on several numerical examples.