An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

Handle URI:
http://hdl.handle.net/10754/624097
Title:
An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Authors:
Karlsson, Peer 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Posters; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorKarlsson, Peer Jesperen
dc.contributor.authorLarsson, Stigen
dc.contributor.authorSandberg, Mattiasen
dc.contributor.authorSzepessy, Andersen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-05T08:35:48Z-
dc.date.available2017-06-05T08:35:48Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624097-
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.en
dc.titleAn A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problemsen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
dc.contributor.institutionKTH Royal Institute of Technologyen
dc.contributor.institutionChalmers University of Technologyen
dc.contributor.institutionUniversity of Gothenburgen
kaust.authorKarlsson, Peer Jesperen
kaust.authorTempone, Raulen
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