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Approximation of Lyapunov functions from noisy data

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Title: Approximation of Lyapunov functions from noisy data
Authors: Giesl, P
Hamzi, B
Rasmussen, M
Webster, KN
Item Type: Journal Article
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.
Issue Date: 1-Jun-2020
Date of Acceptance: 30-Oct-2019
URI: http://hdl.handle.net/10044/1/74379
DOI: 10.3934/jcd.2020003
ISSN: 2158-2491
Publisher: American Institute of Mathematical Sciences
Start Page: 57
End Page: 81
Journal / Book Title: Journal of Computational Dynamics
Volume: 7
Issue: 1
Copyright Statement: © 2020 American Institute of Mathematical Sciences.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/I004165/1
Keywords: math.DS
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences