Second-order viability problems for differential inclusions with endpoint constraint and duality


Mahmudov E.

APPLICABLE ANALYSIS, vol.101, no.3, pp.1130-1146, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 101 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1080/00036811.2020.1773444
  • Journal Name: APPLICABLE ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1130-1146
  • Keywords: 34A60, 49M25, 49N15, 90C46, duality, endpoint constraint, Euler–Lagrange, Infimal convolution, viability
  • Istanbul Technical University Affiliated: Yes

Abstract

The paper deals with the optimal control of second-order viability problems for differential inclusions with endpoint constraint and duality. Based on the concept of infimal convolution and new approach to convex duality functions, we construct dual problems for discrete and differential inclusions and prove the duality results. It seems that the Euler-Lagrange type inclusions are 'duality relations' for both primary and dual problems. Finally, some special cases show the applicability of the general approach; duality in the control problem with second-order polyhedral DFIs and endpoint constraints defined by a polyhedral cone is considered.