Data-Driven Mode Detection and Stabilization of Unknown Switched Linear Systems

Abstract

This article considers the stabilization of unknown switched linear systems using data. Instead of a full system model, we have access to a finite number of trajectories of each of the different modes prior to the online operation of the system. On the basis of informative enough measurements, we design an online switched controller that alternates between a mode detection phase and a stabilization phase. Since the currently active mode is unknown, the controller employs online measurements to determine it by implementing computationally efficient tests that check compatibility with the set of systems consistent with the precollected measurements. The stabilization phase applies a stabilizing feedback gain corresponding to the identified active mode and monitors the evolution of the associated Lyapunov function to detect switches. When a switch is detected, the controller returns to the mode detection phase. Under average dwell- and activation-time assumptions on the switching signal, we show that the proposed controller guarantees a practical stability property of the closed-loop switched system. Various simulations illustrate our results.