Relaxation methods for optimal control problems

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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Bibliographic Details
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
Description
Summary: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.
ISSN:1664-3607
1664-3615

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