Grid refinement in the construction of Lyapunov functions using radial basis functions

Giesl, Peter and Mohammed, Najla (2015) Grid refinement in the construction of Lyapunov functions using radial basis functions. Discrete and Continuous Dynamical Systems - Series B, 20 (8). pp. 2453-2476. ISSN 1531-3492

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Abstract

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.

Item Type: Article
Keywords: Lyapunov function, domain of attraction, mesh-free collocation, Radial Basis Function, Voronoi diagram, refinement
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 29 Oct 2015 13:42
Last Modified: 06 Mar 2017 13:08
URI: http://sro.sussex.ac.uk/id/eprint/57408

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