Verification estimates for the construction of Lyapunov functions using meshfree collocation

Giesl, Peter and Mohammed, Najla (2019) Verification estimates for the construction of Lyapunov functions using meshfree collocation. Discrete and Continuous Dynamical Systems - Series B, 22. ISSN 1531-3492

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Abstract

Lyapunov functions are functions with negative derivative along solutions of a given ordinary differential equation. Moreover, sub-level sets of a Lyapunov function are subsets of the domain of attraction of the equilibrium. One of the numerical construction methods for Lyapunov functions uses meshfree collocation with radial basis functions (RBF). In this paper, we propose two verification estimates combined with this RBF construction method to ensure that the constructed function is a Lyapunov function. We show that this combination of the RBF construction method and the verification estimates always succeeds in constructing and verifying a Lyapunov function for nonlinear ODEs in Rd with an exponentially stable equilibrium.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 10 Oct 2018 08:25
Last Modified: 01 Jul 2019 14:30
URI: http://sro.sussex.ac.uk/id/eprint/79305

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