论文标题
一个用于计算黑色盒子开关线性系统多面体不变的数据驱动的方法
A data-driven method for computing polyhedral invariant sets of black-box switched linear systems
论文作者
论文摘要
在本文中，我们考虑了使用系统轨迹的一组有限的观测值集对黑盒切换线性系统的不变设置计算问题。特别是，本文着重于多面体不变集。我们根据可前进的可达集合提出了一个数据驱动的方法。为了正式验证所提出的方法，我们介绍了$λ$ - 扣除集的概念和切换线性系统几乎不变的集合。开关线性系统的凸面性属性使我们能够对计算集的集合进行收缩分析，并得出概率收缩属性。本着非凸情景优化的精神，我们还建立了固定不变性的机会约束保证。然后，通过数值示例来说明我们的方法的性能。
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.
