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Approximation of reachable sets using optimal control and support vector machines

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Title: Approximation of reachable sets using optimal control and support vector machines
Authors: Rasmussen, M
Rieger, J
Webster, KN
Item Type: Journal Article
Abstract: We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for selected examples.
Issue Date: 15-Jul-2016
Date of Acceptance: 8-Jun-2016
URI: http://hdl.handle.net/10044/1/38647
DOI: https://dx.doi.org/10.1016/j.cam.2016.06.015
ISSN: 0377-0427
Publisher: Elsevier
Start Page: 68
End Page: 83
Journal / Book Title: Journal of Computational and Applied Mathematics
Volume: 311
Copyright Statement: © 2016 Elsevier B.V. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
Funder's Grant Number: EP/L00187X/1
PIEF-GA-2013-624526
Keywords: Numerical & Computational Mathematics
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0906 Electrical And Electronic Engineering
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences