Relaxation methods for optimal control problems

Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

Abstract

We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map ▫$A \colon \mathbb{R}^N \to 2^{\mathbb{R}^N}$▫. We do not assume that ▫$D(A) = \mathbb{R}^N$▫, 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.

Keywords

admissible relaxation;maximal monotone map;Young measure;convex conjugate;weak norm;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.91
COBISS:	18921817
ISSN:	1664-3607
Views:	429
Downloads:	221
Average score:	0 (0 votes)
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