Complete Instability of Differential Inclusions using Lyapunov Methods
Complete Instability of Differential Inclusions using Lyapunov Methods
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使用 Lyapunov 方法的微分包含体的完全不稳定性
DOI：
10.1109/cdc.2018.8618663
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Christopher M. Kellett
中科院分区：
文献类型：
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作者：
P. Braun;L. Grüne;Christopher M. Kellett
李雅普诺夫函数和控制李雅普诺夫函数在分析动态系统的稳定性和设计稳定反馈控制器方面是一个很好的工具。为了解决诸如不安全状态下的稳定或避障等问题，一种潜在的方法是通过反馈使这些障碍变得不稳定。为此，我们引入了（非光滑）Chetaev函数和控制Chetaev函数，并证明了它们对于动力系统完全不稳定性的充分性。虽然“时间反转”方法经常用于研究正向渐近稳定点的逆时不稳定性，但我们通过一个例子证明，这种方法不能通过时间参数中简单的符号变化来从非光滑Lyapunov函数生成Chetaev函数。
Lyapunov functions and control Lyapunov functions are a well established tool in the analysis of stability properties of dynamical systems as well as in the design of stabilizing feedback controllers. In order to address problems such as stabilization in the presence of unsafe sets of states or obstacle avoidance, one potential approach involves rendering such obstacles unstable by feedback. To this end we introduce (nonsmooth) Chetaev and control Chetaev functions and demonstrate their sufficiency for complete instability properties of dynamical systems. While a “time-reversal” approach is frequently used to study instability in reverse time of an asymptotically stable point in forward time, we demonstrate via an example that such an approach cannot be used to generate Chetaev functions from nonsmooth Lyapunov functions via a simple change of sign in the time argument.