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 simulations. 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 concept of almost-invariant sets for switched linear systems. The convexity-preserving property of switched linear systems allows us to conduct contraction analysis on almost-invariant sets and derive an a priori probabilistic guarantee. In the spirit of non-convex scenario optimization, we also establish a posteriori the level of violation on the computed set. The performance of our method is then illustrated by a switched system under arbitrary switching between two modes.

中文翻译：

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一种计算黑盒切换线性系统多面体不变集的数据驱动方法

在本文中，我们仅使用系统模拟的一组有限观测值来考虑黑盒切换线性系统的不变集计算问题。特别是，本文重点研究多面体不变集。我们提出了一种基于一步前可达集的数据驱动方法。为了对所提出的方法进行形式验证，我们引入了切换线性系统的几乎不变集的概念。切换线性系统的凸性保持特性使我们能够对几乎不变的集合进行收缩分析并推导出先验概率保证。本着非凸场景优化的精神，我们还在计算集上建立了后验的违规级别。然后通过在两种模式之间任意切换下的切换系统来说明我们方法的性能。