Data-driven stabilization of switched and constrained linear systems

TL;DR

This paper introduces a data-driven method for stabilizing unknown switched linear systems by designing state feedback controllers using noisy measurements, leveraging Lyapunov inequalities and bilinear programming.

Contribution

It develops a novel data-dependent bilinear programming approach for stabilizing switched systems without assuming mode stabilizability, with computationally efficient relaxations.

Findings

Successfully stabilizes systems using noisy data.

Achieves a good balance between conservatism and computational efficiency.

Demonstrates effectiveness on constrained perturbed systems.

Abstract

We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov-Metzler inequalities, we derive data-dependent bilinear programs whose solution directly returns a provably stabilizing controller and ensures $\mathcal{H}_2$ or $\mathcal{H}_{\infty}$ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for a perturbed linear system. We validate our theoretical findings numerically, demonstrating the favourable trade-off between conservatism and tractability achieved by the proposed relaxations.