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arXiv · 2009.10984

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

Zheming Wang·Raphaël M. Jungers
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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.

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Zheming Wang, Raphaël M. Jungers. 2020-09-23. A data-driven method for computing polyhedral invariant sets of black-box switched linear systems. https://doi.org/10.1109/lcsys.2020.3044838

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