使用无网格配点法构造切换系统的Lyapunov函数
Construction of Lyapunov Functions for Switched Systems using Meshfree Collocation
AI总结：
本文提出一种基于无网格配点法和二次规划的自适应算法，用于构造切换系统的Lyapunov函数并证明其稳定性。
摘要：
切换系统是一类动态系统，其中切换规则指示哪个系统被“开启”。该规则可以依赖于时间和/或状态空间中的位置。切换系统的稳定性通常通过一个（或多个）Lyapunov函数的存在性来研究。我们开发了一种使用散点逼近方法的算法来构造切换系统的Lyapunov函数，并附有稳定性结果。该构造方法改进了先前用于自治常微分方程的方法，该方法使用无网格配点法和二次规划。
英文摘要：
Switched systems are a family of dynamical systems where a switching rule indicates which system is "switched on". This rule can be dependent on time and/or position in the state space. Stability of switched systems is a property that is often investigated using the existence of one (or multiple) Lyapunov function(s). We develop an algorithm using a scattered approximation method to construct a Lyapunov function for switched systems, accompanied with stability results. The construction adapts a previous method for autonomous ODEs that uses meshfree collocation and quadratic programming.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
