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dc.contributor.authorKarlsson, Peer Jesper
dc.contributor.authorLarsson, Stig
dc.contributor.authorSandberg, Mattias
dc.contributor.authorSzepessy, Anders
dc.contributor.authorTempone, Raul
dc.date.accessioned2015-05-25T11:55:27Z
dc.date.available2015-05-25T11:55:27Z
dc.date.issued2015-01
dc.identifier.citationAn Error Estimate for Symplectic Euler Approximation of Optimal Control Problems 2015, 37 (2):A946 SIAM Journal on Scientific Computing
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/140959481
dc.identifier.urihttp://hdl.handle.net/10754/555682
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.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/140959481
dc.relation.urlhttp://arxiv.org/abs/1407.8330
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.titleAn Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentOffice of the VP
dc.contributor.departmentStochastic Numerics Research Group
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, S-412 96 Gothenburg, Sweden
dc.contributor.institutionDepartment of Mathematics, KTH Royal Institute of Technology, S-100 44 Stockholm, Sweden
dc.identifier.arxivid1407.8330
kaust.personKarlsson, Peer Jesper
kaust.personTempone, Raul
dc.versionv1
refterms.dateFOA2018-06-14T07:57:47Z
dc.date.posted2014-07-31


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