Fractional optimal control problem for differential system with delay argument

Advances in Difference Equations

G. Mohamed Bahaa¹ 

[1] Department of Mathematics, Dean of Academic Services, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

关键词: fractional optimal control problems;    fractional differential systems;    time delay;    Dirichlet and Neumann conditions;    existence and uniqueness of solutions;    Riemann-Liouville sense;    Caputo derivative;    46C05;    49J20;    93C20;   

DOI  :  10.1186/s13662-017-1121-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we apply the classical control theory to a fractional differential system in a bounded domain. The fractional optimal control problem (FOCP) for differential system with time delay is considered. The fractional time derivative is considered in a Riemann-Liouville sense. We first study the existence and the uniqueness of the solution of the fractional differential system with time delay in a Hilbert space. Then we show that the considered optimal control problem has a unique solution. The performance index of a FOCP is considered as a function of both state and control variables, and the dynamic constraints are expressed by a partial fractional differential equation. 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 a right fractional Caputo derivative, we obtain an optimality system for the optimal control. Some examples are analyzed in detail.

【 授权许可】

CC BY