Approximation of Lyapunov functions from noisy data

Giesl, Peter, Hamzi, Boumediene, Rasmussen, Martin and Webster, Kevin (2019) Approximation of Lyapunov functions from noisy data. Journal of Computational Dynamics. pp. 1-24. ISSN 2158-2491

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Abstract

Methods have previously been developed for the approximation of Lyapunov functions using radial basis functions. However these methods assume that the evolution equations are known. We consider the problem of approximating a given Lyapunov function using radial basis functions where the evolution equations are not known, but we instead have sampled data which is contaminated with noise. We propose an algorithm in which we first approximate the underlying vector field, and use this approximation to then approximate the Lyapunov function. Our approach combines elements of machine learning/ statistical learning theory with the existing theory of Lyapunov function approximation. Error estimates are provided for our algorithm.

Item Type: Article
Keywords: Lyapunov function, differential equations, radial basis function, error estimates, reproducing kernel Hilbert space
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Amelia Redman
Date Deposited: 04 Nov 2019 08:38
Last Modified: 24 Jan 2020 14:30
URI: http://sro.sussex.ac.uk/id/eprint/87748

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