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Authors: Peter Giesl 1 and Najla Mohammed 2

Affiliations: 1 Department of Mathematics, University of Sussex, Falmer, BN1 9QH and U.K. ; 2 Department of Mathematical Sciences, Umm Al-Qura University, Makkah and Saudi Arabia

ISBN: 978-989-758-321-6

Keyword(s): Lyapunov Function, Domain of Attraction, Radial Basis Function, Refinement Algorithm, Verification Estimates.

Abstract: Lyapunov functions are an important tool for the determination of the domain of attraction of an equilibrium point of a given ordinary differential equation. The Radial Basis Functions collocation method is one of the numerical methods to construct Lyapunov functions. This method has been improved by combining it with a refinement algorithm to reduce the number of collocation points required in the construction process, as well as a verification that the constructed function is a Lyapunov function. In this paper, we propose a combination of both methods in one, called the combination method. This method constructs a Lyapunov function with the refinement algorithm and then verifies its properties rigorously. The method is illustrated with examples.

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Paper citation in several formats:
Giesl, P. and Mohammed, N. (2018). Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions.In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE, ISBN 978-989-758-321-6, pages 569-578. DOI: 10.5220/0006944405690578

@conference{ctde18,
author={Peter Giesl. and Najla Mohammed.},
title={Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions},
booktitle={Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE,},
year={2018},
pages={569-578},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006944405690578},
isbn={978-989-758-321-6},
}

TY - CONF

JO - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE,
TI - Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions
SN - 978-989-758-321-6
AU - Giesl, P.
AU - Mohammed, N.
PY - 2018
SP - 569
EP - 578
DO - 10.5220/0006944405690578

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