Relaxation methods for optimal control problems

We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map A : ℝN → 2ℝN. We do not assume that D(A) = ℝN, incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The f...

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Main Authors:	Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
Format:	Article
Language:	English
Published:	World Scientific Publishing 2020-04-01
Series:	Bulletin of Mathematical Sciences
Subjects:	admissible relaxation maximal monotone map young measure convex conjugate weak norm
Online Access:	http://www.worldscientific.com/doi/pdf/10.1142/S1664360720500046

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spelling	doaj-27ede68257a44fde9efe5ca2e6d817662020-11-25T03:16:26ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152020-04-011012050004-12050004-2410.1142/S166436072050004610.1142/S1664360720500046Relaxation methods for optimal control problemsNikolaos S. Papageorgiou0Vicenţiu D. Rădulescu1Dušan D. Repovš2Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, GreeceInstitute of Mathematics, Physics and Mechanics, 1000 Ljubljana, SloveniaInstitute of Mathematics, Physics and Mechanics, 1000 Ljubljana, SloveniaWe consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map A : ℝN → 2ℝN. We do not assume that D(A) = ℝN, incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.http://www.worldscientific.com/doi/pdf/10.1142/S1664360720500046admissible relaxationmaximal monotone mapyoung measureconvex conjugateweak norm
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nikolaos S. Papageorgiou Vicenţiu D. Rădulescu Dušan D. Repovš
spellingShingle	Nikolaos S. Papageorgiou Vicenţiu D. Rădulescu Dušan D. Repovš Relaxation methods for optimal control problems Bulletin of Mathematical Sciences admissible relaxation maximal monotone map young measure convex conjugate weak norm
author_facet	Nikolaos S. Papageorgiou Vicenţiu D. Rădulescu Dušan D. Repovš
author_sort	Nikolaos S. Papageorgiou
title	Relaxation methods for optimal control problems
title_short	Relaxation methods for optimal control problems
title_full	Relaxation methods for optimal control problems
title_fullStr	Relaxation methods for optimal control problems
title_full_unstemmed	Relaxation methods for optimal control problems
title_sort	relaxation methods for optimal control problems
publisher	World Scientific Publishing
series	Bulletin of Mathematical Sciences
issn	1664-3607 1664-3615
publishDate	2020-04-01
description	We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map A : ℝN → 2ℝN. We do not assume that D(A) = ℝN, incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.
topic	admissible relaxation maximal monotone map young measure convex conjugate weak norm
url	http://www.worldscientific.com/doi/pdf/10.1142/S1664360720500046
work_keys_str_mv	AT nikolaosspapageorgiou relaxationmethodsforoptimalcontrolproblems AT vicentiudradulescu relaxationmethodsforoptimalcontrolproblems AT dusandrepovs relaxationmethodsforoptimalcontrolproblems
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Relaxation methods for optimal control problems

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