Computing an invariance kernel with target by computing Lyapunov-like functions
Computing an invariance kernel with target by computing Lyapunov-like functions
复制标题
通过计算类 Lyapunov 函数来计算具有目标的不变性核
DOI：
10.1049/iet-cta.2013.0275
复制
发表时间：
2013
影响因子：
2.6
通讯作者：
Xue Bai
中科院分区：
文献类型：
--
作者：
She Zhikun;Xue Bai
可达性分析和生存性理论在约束动力系统的控制综合和轨迹分析中起着重要的作用，许多方法已知用于计算低维非线性系统，但这些众所周知的方法依赖于状态空间的网格化，因此遭受维数灾难。在这项研究中，其动态由多项式描述的系统，提出了一种基于半定规划的方法，通过迭代搜索类李雅普诺夫函数来估计目标尽可能大的不变核。所提出的方法是可扩展的，因为要解决的半定规划问题的大小随系统维数线性增长。通过两个有趣的例子对该方法进行了测试，并与现有的一些方法进行了比较，结果表明该方法是有效的。
Reachability analysis and viability theory play an important role in control synthesis and trajectory analysis of constrained dynamical systems, many methods are known for computing them in low‐dimensional non‐linear systems, but these well‐known methods rely on gridding the state space and hence suffer from the curse of dimensionality. In this study, for systems whose dynamics are described by polynomials, a method based on semi‐definite programming is proposed to estimate an invariance kernel with target as large as possible by iteratively searching for Lyapunov‐like functions. The proposed methodology is scalable, since the size of the semi‐definite programming problem to be solved grows linearly with the system dimension. We test the method on two interesting examples and compare them with some existing methods, the results show that our method is more efficient.