Optimal control problem for variable-order fractional differential systems with time delay involving Atangana–Baleanu derivatives
| Autor: | G. M. Bahaa |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Generalization
General Mathematics Applied Mathematics Control variable General Physics and Astronomy Boundary (topology) Statistical and Nonlinear Physics Function (mathematics) Optimal control 01 natural sciences 010305 fluids & plasmas Fractional calculus 0103 physical sciences Time derivative Applied mathematics Uniqueness 010301 acoustics Mathematics |
| Zdroj: | Chaos, Solitons & Fractals. 122:129-142 |
| ISSN: | 0960-0779 |
| DOI: | 10.1016/j.chaos.2019.03.001 |
| Popis: | The Optimal Control Problem (OCP) for variable-order fractional differential systems with time delay is considered. The fractional time derivative is Atangana–Baleanu derivatives in a Caputo sense. The existence and the uniqueness results are derived. Then we show that the considered optimal control problem has a unique solution. The performance index of a (FOCP) is considered as an integral function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) with variable-order and time delay. The time horizon is fixed. Finally, we impose some constraints on the boundary control. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of right fractional Atangana–Baleanu derivative, we obtain an optimality system for the optimal control. To obtain the optimality conditions for the given problem, the generalization of the Dubovitskii–Milyutin Theorem was applied. To illustrate the results we introduce some examples. |
| Databáze: | OpenAIRE |
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