In this letter, 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 letter 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.

中文翻译：

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黑盒切换线性系统的多面体不变集的数据驱动方法

在这封信中，我们仅使用系统轨迹的有限观测值，考虑了黑盒切换线性系统的不变集计算问题。特别是，这封信着重于多面体不变集。我们提出了一种基于数据的方法，该方法基于一步向前的可到达集合。为了对所提出的方法进行形式验证，我们介绍了交换线性系统的\\ lambda $-压缩集和几乎不变集的概念。切换线性系统的保凸性使我们能够对计算集进行收缩分析并得出概率收缩性质。本着非凸场景优化的精神，我们还针对集合不变性建立了机会受限的保证。然后，通过数值示例说明了我们方法的性能。