论文标题
学习稳定性保证数据驱动的受限开关线性系统
Learning stability guarantees for data-driven constrained switching linear systems
论文作者
论文摘要
我们考虑对受约束开关的线性系统的稳定性分析，其中动态是未知的，其开关信号受自动机的约束。我们提出了一个数据驱动的Lyapunov框架，用于根据系统观察结果收获的数据提供概率稳定性保证。通过将先前的结果推广到任意切换线性系统上，我们表明，通过对有限数量的观测值进行采样，我们能够为基础系统构建近似Lyapunov函数。此外，我们表明自动机接受的语言的熵允许绑定所需的样本数量以达到某些预先指定的准确性。
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic stability guarantees based on data harvested from observations of the system. By generalizing previous results on arbitrary switching linear systems, we show that, by sampling a finite number of observations, we are able to construct an approximate Lyapunov function for the underlying system. Moreover, we show that the entropy of the language accepted by the automaton allows to bound the number of samples needed in order to reach some pre-specified accuracy.
