@inproceedings{7fb9b2a1d7cd4e8ab5936d7287e2ccf3,
title = "Clustering algorithm for generalized recurrences using complete Lyapunov functions",
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.",
keywords = "Chain-recurrent set, Clustering algorithm, Complete Lyapunov functions, Dynamical systems, Mathematics",
author = "Carlos Arg{\'a}ez and Peter Giesl and Sigurdur Hafstein",
note = "Publisher Copyright: Copyright {\textcopyright} 2019 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.; 16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019 ; Conference date: 29-07-2019 Through 31-07-2019",
year = "2019",
doi = "10.5220/0007934101380146",
language = "English",
series = "ICINCO 2019 - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics",
publisher = "SciTePress",
pages = "138--146",
editor = "Oleg Gusikhin and Kurosh Madani and Janan Zaytoon",
booktitle = "ICINCO 2019 - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics",
}