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

共 50 条

[31] Approximation of insurance liability contracts using radial basis functions
Singor, Stefan N.
Schols, Eric
Oosterlee, Cornelis W.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (11) : 2245 - 2271
[32] Using radial basis functions to construct local volatility surfaces
Glover, J.
Ali, M. M.
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (09) : 4834 - 4839
[33] Parallel Stochastic Global Optimization Using Radial Basis Functions
Regis, Rommel G.
Shoemaker, Christine A.
INFORMS JOURNAL ON COMPUTING, 2009, 21 (03) : 411 - 426
[34] Implicit fitting using radial basis functions with ellipsoid constraint
Li, Q
Wills, D
Phillips, R
Viant, WJ
Griffiths, JG
Ward, J
COMPUTER GRAPHICS FORUM, 2004, 23 (01) : 55 - 69
[35] SOLUTIONS TO PSEUDODIFFERENTIAL EQUATIONS USING SPHERICAL RADIAL BASIS FUNCTIONS
Pham, T. D.
Tran, T.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 79 (03) : 473 - 485
[36] Dynamics Identification in Evolution Models Using Radial Basis Functions
Merger, Juri
Borzi, Alfio
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2017, 23 (02) : 317 - 335
[37] Radial polynomials as alternatives to flat radial basis functions
Pooladi, Fatemeh
Hosseinzadeh, Hossein
JOURNAL OF MATHEMATICAL MODELING, 2024, 12 (02): : 337 - 354
[38] A METHOD FOR CONSTRUCTION OF STABILITY REGIONS BY LYAPUNOV FUNCTIONS
KAMENETSKIY, VA
SYSTEMS & CONTROL LETTERS, 1995, 26 (02) : 147 - 151
[39] Construction of Lyapunov Functions using Multi-Objective Genetic Algorithm
Sabouri, Mohammad
Setoodeh, Peyman
Asemani, Mohammad Hassan
2020 28TH IRANIAN CONFERENCE ON ELECTRICAL ENGINEERING (ICEE), 2020, : 818 - 822
[40] On Definition and Construction of Lyapunov Functions for Boolean Networks
Wang, Yuzhen
Li, Haitao
PROCEEDINGS OF THE 10TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA 2012), 2012, : 1247 - 1252

← 1 2 3 4 5 →