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An error estimate for symplectic euler approximation of optimal control problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0003-2669-359X
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
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2015 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 37, no 2, A946-A969 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 37, no 2, A946-A969 p.
Keyword [en]
optimal control, error estimates, adaptivity, error control
National Category
URN: urn:nbn:se:kth:diva-169160DOI: 10.1137/140959481ISI: 000353838400016ScopusID: 2-s2.0-84928978705OAI: diva2:820483
Swedish Research CouncilSwedish eā€Science Research Center

QC 20150612

Available from: 2015-06-12 Created: 2015-06-11 Last updated: 2015-06-12Bibliographically approved

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Sandberg, MattiasSzepessy, Anders
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