10-3934-dcdsb-2015-20-2453-post-ref-version.pdf (1.36 MB)
Grid refinement in the construction of Lyapunov functions using radial basis functions
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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series BISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
8Volume
20Page range
2453-2476Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2015-10-29First Open Access (FOA) Date
2016-11-01First Compliant Deposit (FCD) Date
2015-10-29Usage metrics
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