OPTIMALITY CONDITIONS OF SINGULAR CONTROLS FOR SYSTEMS WITH CAPUTO FRACTIONAL DERIVATIVES

Yusubov S. S., Mahmudov E.

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, vol.19, pp.246-264, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19
  • Publication Date: 2023
  • Doi Number: 10.3934/jimo.2021182
  • Journal Name: JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
  • Page Numbers: pp.246-264
  • Keywords: Fractional derivative, optimal control, representation formula, Pon-tryagin maximum principle, second-order necessary condition, DIFFERENTIAL EQUATIONS, DUALITY, ORDER
  • Istanbul Technical University Affiliated: Yes

Abstract

In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equa-tion. The problem is investigated in the case when the Pontryagin maximum principle degenerates, that is, it is satisfied trivially. Then the second order optimality conditions are derived for the considered problem.