First- and Second-Order Necessary Optimality Conditions for a Control Problem Described by Nonlinear Fractional Difference Equations

Aliyeva S.

Automation and Remote Control, vol.84, no.3, pp.187-195, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Nəşrin Növü: Article / Article
  • Cild: 84 Say: 3
  • Nəşr tarixi: 2023
  • Doi nömrəsi: 10.1134/s0005117923030025
  • jurnalın adı: Automation and Remote Control
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Səhifə sayı: pp.187-195
  • Açar sözlər: admissible control, analog of the Euler equation, fractional difference equation, fractional operator, fractional sum, open set, optimal control
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

Abstract: This paper considers an optimal control problem for an object described by a system of nonlinear fractional difference equations. Such problems are a discrete analog of optimal control problems described by fractional ordinary differential equations. The first and second variations of a performance criterion are calculated using a modification of the increment method under the assumption that the control set is open. We establish a first-order necessary optimality condition (an analog of the Euler equation) and a general second-order necessary optimality condition. Adopting the representations of the solution of the linearized fractional difference equations from the general second-order optimality condition, we derive necessary optimality conditions in terms of the original problem parameters. Finally, with a special choice of an admissible variation of control, we formulate a pointwise necessary optimality condition for classical extremals.