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- Title
First- and Second-Order Necessary Optimality Conditions for a Control Problem Described by Nonlinear Fractional Difference Equations.
- Authors
Aliyeva, S. T.
- 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.
- Subjects
NONLINEAR difference equations; NONLINEAR equations; ORDINARY differential equations; FRACTIONAL differential equations; EULER equations; DIFFERENCE equations
- Publication
Automation & Remote Control, 2023, Vol 84, Issue 3, p187
- ISSN
0005-1179
- Publication type
Article
- DOI
10.1134/S0005117923030025