OPTIMALITY CONDITIONS OF SINGULAR CONTROLS FOR SYSTEMS WITH CAPUTO FRACTIONAL DERIVATIVES

Yusubov S. S. , Mahmudov E.

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2021 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.3934/jimo.2021182
  • Title of Journal : JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
  • Keywords: Fractional derivative, optimal control, representation formula, Pon-tryagin maximum principle, second-order necessary condition, DIFFERENTIAL EQUATIONS, DUALITY, ORDER

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.