Giesl, Peter, Hamzi, Boumediene, Rasmussen, Martin and Webster, Kevin (2020) Approximation of Lyapunov functions from noisy data. Journal of Computational Dynamics, 7 (1). pp. 57-81. 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 |
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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: | 25 Dec 2020 02:00 |
URI: | http://sro.sussex.ac.uk/id/eprint/87748 |
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