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

Najla A. Mohammed | Zendy; Peter Giesl | Zendy

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

Author(s) -

Najla A. Mohammed,

Peter Giesl

Publication year - 2015

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2015.20.2453

Subject(s) - lyapunov function , voronoi diagram , grid , lyapunov equation , lyapunov optimization , construct (python library) , lyapunov redesign , computer science , domain (mathematical analysis) , basis (linear algebra) , mathematics , function (biology) , control lyapunov function , mathematical optimization , lyapunov exponent , algorithm , mathematical analysis , artificial intelligence , geometry , nonlinear system , physics , quantum mechanics , chaotic , programming language , evolutionary biology , biology

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.

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