Authors:
Carlos Argáez
1
;
Peter Giesl
2
and
Sigurdur Hafstein
1
Affiliations:
1
Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík and Iceland
;
2
Department of Mathematics, University of Sussex, Falmer, BN1 9QH and U.K.
Keyword(s):
Complete Lyapunov Functions, Chain-recurrent Set, Clustering Algorithm, Mathematics, Dynamical Systems.
Related
Ontology
Subjects/Areas/Topics:
Informatics in Control, Automation and Robotics
;
Intelligent Control Systems and Optimization
;
Optimization Algorithms
Abstract:
Many advances and algorithms have been proposed to obtain complete Lyapunov functions for dynamical systems and to properly describe the chain-recurrent set, e.g. periodic orbits. Recently, a heuristic algorithm was proposed to classify and reduce the over-estimation of different periodic orbits in the chain-recurrent set, provided they are circular. This was done to investigate the effect on further iterations of the algorithm to compute approximations to a complete Lyapunov function. In this paper, we propose an algorithm that classifies the different connected components of the chain-recurrent set for general systems, not restricted to (circular) periodic orbits. The algorithm is based on identifying clustering of points and is independent of the particular algorithm to construct the complete Lyapunov functions.