GRID REFINEMENT IN THE CONSTRUCTION OF LYAPUNOV FUNCTIONS USING RADIAL BASIS FUNCTIONS

被引：6

作者：

Mohammed, Najla ^{[1
]}

Giesl, Peter ^{[1
]}

机构：

[1] Univ Sussex, Dept Math, Falmer BN1 9QH, E Sussex, England

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2015年 / 20卷 / 08期

基金：

英国工程与自然科学研究理事会;

关键词：

Lyapunov function; domain of attraction; mesh-free collocation; Radial Basis Function; Voronoi diagram; refinement; INTERPOLATION;

D O I：

10.3934/dcdsb.2015.20.2453

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Lyapunov functions are a main tool to determine the domain of attraction of equilibria in dynamical systems. Recently, several methods have been presented to construct a Lyapunov function for a given system. In this paper, we improve the construction method for Lyapunov functions using Radial Basis Functions. We combine this method with a new grid refinement algorithm based on Voronoi diagrams. Starting with a coarse grid and applying the refinement algorithm, we thus manage to reduce the number of data points needed to construct Lyapunov functions. Finally, we give numerical examples to illustrate our algorithms.

引用

页码：2453 / 2476

页数：24

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