Optimal Control of Ordinary Fractional-Order Systems With a Delay in the Phase Variable

Yusubov S. S., Mahmudov E., Yusubov S. S.

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1002/mma.70219
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Caputo derivative, fractional optimal control, necessary optimality condition
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

The paper considers a fractional model described by the Bolza problem of optimal control with delay in the phase variable depending on the fractional Caputo derivative of order (Formula presented.) and the fractional Riemann–Liouville integral of order (Formula presented.). For the problem posed, a necessary optimality condition in the form of the Pontryagin maximum principle is formulated. Moreover, for the control, which is singular, a necessary optimality condition of a higher order is obtained for the first time. Unlike previous works, the results are formulated for both conditions (Formula presented.) and (Formula presented.). The effectiveness of the available results is illustrated by specific examples.