An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

Handle URI:
http://hdl.handle.net/10754/555682
Title:
An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Authors:
Karlsson, Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Citation:
An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems 2015, 37 (2):A946 SIAM Journal on Scientific Computing
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
Jan-2015
DOI:
10.1137/140959481
ARXIV:
arXiv:1407.8330
Type:
Article
ISSN:
1064-8275; 1095-7197
Additional Links:
http://epubs.siam.org/doi/10.1137/140959481; http://arxiv.org/abs/1407.8330
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKarlsson, Jesperen
dc.contributor.authorLarsson, Stigen
dc.contributor.authorSandberg, Mattiasen
dc.contributor.authorSzepessy, Andersen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-05-25T11:55:27Zen
dc.date.available2015-05-25T11:55:27Zen
dc.date.issued2015-01en
dc.identifier.citationAn Error Estimate for Symplectic Euler Approximation of Optimal Control Problems 2015, 37 (2):A946 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/140959481en
dc.identifier.urihttp://hdl.handle.net/10754/555682en
dc.description.abstractThis work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/140959481en
dc.relation.urlhttp://arxiv.org/abs/1407.8330en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.titleAn Error Estimate for Symplectic Euler Approximation of Optimal Control Problemsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, S-412 96 Gothenburg, Swedenen
dc.contributor.institutionDepartment of Mathematics, KTH Royal Institute of Technology, S-100 44 Stockholm, Swedenen
dc.identifier.arxividarXiv:1407.8330en
kaust.authorKarlsson, Peer Jesperen
kaust.authorTempone, Raulen
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