论文标题
通过Lyapunov函数的匡威屏障功能
Converse Barrier Functions via Lyapunov Functions
论文作者
论文摘要
我们通过Converse Lyapunov理论证明了强大的匡威屏障函数定理。尽管使用Lyapunov函数作为屏障函数很简单，但存在Converse Lyapunov函数作为给定安全集的屏障函数并非如此。我们通过强大的论点建立了这种链接。我们表明，在轻度的技术假设下，坚固安全集合的前进式固定集必须稳定稳定。结果，所有健壮的安全动力学系统都必须以lyapunov函数的形式接受稳定的屏障功能，以进行设置稳定性。我们在连续时间和离散时间设置中介绍了结果，并发表了有关与各种屏障函数条件的连接的评论。
We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a given safety set is not. We establish this link by a robustness argument. We show that the closure of the forward reachable set of a robustly safe set must be robustly asymptotically stable under mild technical assumptions. As a result, all robustly safe dynamical systems must admit a robust barrier function in the form of a Lyapunov function for set stability. We present the results in both continuous-time and discrete-time settings and remark on connections with various barrier function conditions.
