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

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.

To appear in IEEE Control Systems Letters

References in corpus (2)

• Data-driven computation of invariant sets of discrete time-invariant black-box systems
• Computation of the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints

Cited by in corpus (2)

• Chance-constrained quasi-convex optimization with application to data-driven switched systems control
• Probabilistic stabilizability certificates for a class of black-box linear systems