论文标题
具有样本的多个Lyapunov功能的混合系统的黑盒稳定性分析
Black-box stability analysis of hybrid systems with sample-based multiple Lyapunov functions
论文作者
论文摘要
我们提出了一个基于多个Lyapunov函数的框架，以查找概率数据驱动的保证，以确保未知约束开关线性系统（CSL）的稳定性，它们是开关线性系统的切换信号由自动机限制的线性系统。 CSL的稳定性的特征在于其约束的关节半径（CJSR）。受到场景方法的启发和以前的不受约束开关系统的工作，我们表征了使用CJSR概念在CSL上找到足够的（IN-）稳定性所需的观测值。更确切地说，我们的贡献是：我们从有限数量的观测值中得出了一个未知CSL的概率上限。我们还得出了CJSR上的确定性下限。从中，我们获得了一种概率方法来表征未知CSL的稳定性。
We present a framework based on multiple Lyapunov functions to find probabilistic data-driven guarantees on the stability of unknown constrained switching linear systems (CSLS), which are switching linear systems whose switching signal is constrained by an automaton. The stability of a CSLS is characterized by its constrained joint spectral radius (CJSR). Inspired by the scenario approach and previous work on unconstrained switching systems, we characterize the number of observations needed to find sufficient conditions on the (in-)stability of a CSLS using the notion of CJSR. More precisely, our contribution is the following: we derive a probabilistic upper bound on the CJSR of an unknown CSLS from a finite number of observations. We also derive a deterministic lower bound on the CJSR. From this we obtain a probabilistic method to characterize the stability of an unknown CSLS.
