Using data informativity for online stabilization of unknown switched linear systems

TL;DR

This paper presents a data-driven method for stabilizing unknown switched linear systems by designing a controller that identifies active modes from noiseless measurements and switches accordingly, ensuring stability under certain switching conditions.

Contribution

It introduces a novel data-driven switched controller that stabilizes systems without full dynamics knowledge, using measurements collected during an initialization phase.

Findings

Controller stabilizes systems under specified switching conditions.

Simulation results demonstrate effectiveness on a network example.

Method enables stabilization with limited measurement data.

Abstract

This work studies data-driven switched controller design for discrete-time switched linear systems. Instead of having access to the full system dynamics, an initialization phase is performed, during which noiseless measurements of the state and the input are collected for each mode. Under certain conditions on these measurements, we develop a stabilizing switched controller for the switched system. To be precise, the controller switches between identifying the active mode of the system and applying a predetermined stabilizing feedback. We prove that if the system switches according to certain specifications, this controller stabilizes the closed-loop system. Simulations on a network example illustrate our approach.