Pontryagin's maximum principle for the Roesser model with a fractional Caputo derivative

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Yusubov S. S., Mahmudov E.

ARCHIVES OF CONTROL SCIENCES, vol.34, no.2, pp.271-300, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.24425/acs.2024.149661
  • Journal Name: ARCHIVES OF CONTROL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.271-300
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this paper, we study the modern mathematical theory of the optimal control problem associated with the fractional Roesser model and described by Caputo partial derivatives, where the functional is given by the Riemann-Liouville fractional integral. In the formulated problem, a new version of the increment method is applied, which uses the concept of an adjoint integral equation. Using the Banach fixed point principle, we prove the existence and uniqueness of a solution to the adjoint problem. Then the necessary and sufficient optimality condition is derived in the form of the Pontryagin's maximum principle. Finally, the result obtained is illustrated by a concrete example.