Clustering Algorithm for Generalized Recurrences using Complete Lyapunov Functions

Carlos Argáez, Peter Giesl, Sigurdur Hafstein

2019

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.

Paper Citation

in Harvard Style

Argáez C., Giesl P. and Hafstein S. (2019). Clustering Algorithm for Generalized Recurrences using Complete Lyapunov Functions.In Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-380-3, pages 138-146. DOI: 10.5220/0007934101380146

in Bibtex Style

@conference{icinco19,
author={Carlos Argáez and Peter Giesl and Sigurdur Hafstein},
title={Clustering Algorithm for Generalized Recurrences using Complete Lyapunov Functions},
booktitle={Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2019},
pages={138-146},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007934101380146},
isbn={978-989-758-380-3},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Clustering Algorithm for Generalized Recurrences using Complete Lyapunov Functions
SN - 978-989-758-380-3
AU - Argáez C.
AU - Giesl P.
AU - Hafstein S.
PY - 2019
SP - 138
EP - 146
DO - 10.5220/0007934101380146