SOME NECESSARY OPTIMALITY CONDITIONS FOR SYSTEMS WITH FRACTIONAL CAPUTO DERIVATIVES

Yusubov S. S., Mahmudov E.

Journal of Industrial and Management Optimization, vol.19, no.12, pp.8831-8850, 2023 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 19 Say: 12
  • Nəşr tarixi: 2023
  • Doi nömrəsi: 10.3934/jimo.2023063
  • jurnalın adı: Journal of Industrial and Management Optimization
  • Jurnalın baxıldığı indekslər: 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
  • Səhifə sayı: pp.8831-8850
  • Açar sözlər: Fractional Caputo derivative, fractional optimal control, necessary optimality condition
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First, an analogue of the Pontryagin maximum principle is obtained, and in the case of the degeneration of the Pontryagin maximum principle, a high-order necessary optimality condition is obtained. Further, if the control under study lies inside the set of restrictions on the control, then we obtain an analogue of the Euler equation, an analogue of the Legendre-Clebsch condition, and when the Legendre-Clebsch condition degenerates, we obtain the necessary high-order optimality condition.