Improved estimation of the chain-recurrent set

Argaez, Carlos, Giesl, Peter and Hafstein, Sigurdur Freyr (2019) Improved estimation of the chain-recurrent set. In: 2019 18th European Control Conference (ECC). IEEE, pp. 1622-1627. ISBN 9783907144008

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Abstract

When studying the behaviour of dynamical systems, one particular goal is to find and isolate the periodic solutions and the equilibria. They are a subset of the chain-recurrent set of the dynamical system. In recent work, many improvements have been achieved in computing an approximation of a complete Lyapunov function of a given dynamical system and thus to identify the chain-recurrent set. A weak point in this approach, however, has been an over-estimation of the chain-recurrent set. In this work, we introduce a heuristic algorithm that reduces the overestimation in a simple and efficient way. Furthermore, a new and improved grid to evaluate the complete Lyapunov function is introduced to avoid unevaluated regions in the domain of the function.

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 24 Jun 2022 10:32
Last Modified: 24 Jun 2022 10:32
URI: http://sro.sussex.ac.uk/id/eprint/106591

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