Inner approximations of domains of attraction for a class of switched systems by computing Lyapunov-like functions
Inner approximations of domains of attraction for a class of switched systems by computing Lyapunov-like functions
复制标题
通过计算类李雅普诺夫函数来对一类切换系统的吸引域进行内近似
DOI：
10.1002/rnc.4010
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发表时间：
--
影响因子：
3.9
通讯作者：
Meilun Li
中科院分区：
文献类型：
--
作者：
Xiuliang Zheng;Zhikun She;Quanyi Liang;Meilun Li
吸引域在控制系统分析中起着重要的作用，通常用李雅普诺夫函数的子水平集来估计。本文基于公共Lyapunov - like函数的概念，提出了一种估计一类切换系统吸引域的迭代方法，该系统的状态空间被划分为若干区域，每个区域用多项式不等式描述，并且任何区域之间都没有交集。从吸引域的初始内估计开始，我们首先提出了一个理论框架，通过迭代计算常见的Lyapunov - like函数来获得更大的内估计。然后，为了获得吸引域的初始内估计，我们提出了一种基于高阶截断和线性半定规划的计算公共Lyapunov函数的方法。随后，利用S过程和平方和规划，结合坐标迭代思想，对理论框架进行了近似实现。最后，我们实现了我们的方法，并在一些实例上进行了对比测试。计算和比较结果表明了该方法的优越性。
Domain of attraction plays an important role in control systems analysis, which is usually estimated by sublevel sets of Lyapunov functions. In this paper, based on the concept of common Lyapunov‐like functions, we propose an iteration method for estimating domains of attraction for a class of switched systems, where the state space is divided into several regions, each region is described by polynomial inequalities, and any region has no intersection among with each other. Starting with an initial inner estimate of domain of attraction, we first present a theoretical framework for obtaining a larger inner estimate by iteratively computing common Lyapunov‐like functions. Then, for obtaining a required initial inner estimate of domain of attraction, we propose a higher‐order truncation and linear semidefinite programming–based method for computing a common Lyapunov function. Successively, the theoretical framework is under‐approximatively realized by using S‐procedure and sum‐of‐squares programming, associated with a coordinatewise iteration idea. Finally, we implement our method and test it on some examples with comparisons. These computation and comparison results show the advantages of our method.