Relaxation methods for optimal control problems

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

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.

• Language: English
• Keywords: admissible relaxation, maximal monotone map, Young measure, convex conjugate, weak norm
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: art. 2050004 (24 str.)
• Numbering: Vol. 10, iss. 1
• PID: 20.500.12556/RUL-116487
• UDC: 517.91
• ISSN on article: 1664-3607
• DOI: 10.1142/S1664360720500046
• COBISS.SI-ID: 18921817
• Publication date in RUL: 25.05.2020

Record is a part of a journal

• Title: Bulletin of mathematical sciences
• Shortened title: Bull. math. sci.
• Publisher: Springer International Publishing
• ISSN: 1664-3607
• COBISS.SI-ID: 18343257