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

arXiv: https://arxiv.org/abs/2009.10984 · HTML: https://mlsanity.com/paper/2009.10984/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]](https://mlsanity.com/paper/2303.17618/) (2023)

## Abstract (arXiv)

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 λ-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.