A data-driven method for computing polyhedral invariant sets of black-box switched linear systems

TL;DR

This paper introduces a data-driven approach to compute polyhedral invariant sets for black-box switched linear systems using finite trajectory observations, with probabilistic guarantees and contraction analysis.

Contribution

It presents a novel method leveraging one-step reachable sets and scenario optimization for invariant set computation in black-box systems.

Findings

Method successfully computes invariant sets with probabilistic guarantees.

Convexity-preserving property enables contraction analysis.

Numerical examples demonstrate effectiveness of the approach.

Abstract

In this paper, we consider the problem of invariant set computation for black-box switched linear systems using merely a finite set of observations of system trajectories. In particular, this paper focuses on polyhedral invariant sets. We propose a data-driven method based on the one step forward reachable set. For formal verification of the proposed method, we introduce the concepts of $\lambda$-contractive sets and almost-invariant sets for switched linear systems. The convexity-preserving property of switched linear systems allows us to conduct contraction analysis on the computed set and derive a probabilistic contraction property. In the spirit of non-convex scenario optimization, we also establish a chance-constrained guarantee on set invariance. The performance of our method is then illustrated by numerical examples.