Optimal control of differential inclusions with endpoint constraints and duality

Mahmudov E.

APPLICABLE ANALYSIS, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1080/00036811.2022.2136073
  • 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
  • Keywords: Endpoint constraints, Hamiltonian, necessary and sufficient, duality, support function, Euler-Lagrange, 2ND-ORDER, OPTIMIZATION, CONTROLLABILITY, EXISTENCE, DISCRETE
  • Istanbul Technical University Affiliated: Yes

Abstract

The article considers a high-order optimal control problem and its dual problems described by high-order differential inclusions. In this regard, the established Euler-Lagrange type inclusion, containing the Euler-Poisson equation of the calculus of variations, is a sufficient optimality condition for a differential inclusion of a higher order. It is shown that the adjoint inclusion for the first-order differential inclusions, defined in terms of a locally adjoint mapping, coincides with the classical Euler-Lagrange inclusion. Then the duality theorems are proved.