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.
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This paper was recommended for publication by A.G. Kushner, a member of the Editorial Board
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Aliyeva, S.T. First- and Second-Order Necessary Optimality Conditions for a Control Problem Described by Nonlinear Fractional Difference Equations. Autom Remote Control 84, 187–195 (2023). https://doi.org/10.1134/S0005117923030025
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DOI: https://doi.org/10.1134/S0005117923030025