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

作者：Mohammed Najla^*; Giesl Peter

来源：Discrete and Continuous Dynamical Systems-Series B, 2015, 20(8): 2453-2476.

DOI：10.3934/dcdsb.2015.20.2453

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

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.

• 出版日期2015-10