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Approximation of Lyapunov functions from noisy data
journal contribution
posted on 2023-06-09, 19:32 authored by Peter GieslPeter Giesl, Boumediene Hamzi, Martin Rasmussen, Kevin WebsterMethods 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Journal of Computational DynamicsISSN
2158-2491Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
1Volume
7Page range
57-81Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-11-04First Open Access (FOA) Date
2020-12-25First Compliant Deposit (FCD) Date
2019-11-01Usage metrics
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