Using the Integral Operational Matrix of B-Spline Functions to Solve Fractional Optimal Control Problems

In this paper‎, ‎we present a numerical method for solving the fractional optimal control problems in which fractional integral operational matrices of basic B-spline functions are used‎. ‎In the proposed method‎, ‎we use the Riemann-Liouville fractional integral‎. ‎With the help of the operational matrix of the fractional integral and the collocation method‎, ‎we transform the fractional optimal control problem into a nonlinear programming problem‎ ‎and then solve it with an appropriate optimization algorithm‎. ‎Compared to similar numerical techniques‎, ‎our method has better accuracy and efficiency, and also it is easy to use‎. ‎To provide a clear view of the applicability and efficiency of our numerical method‎, several illustrative examples are presented.

Keywords:

Fractional optimal control problem‎ , ‎Riemann-Leiville fractional integral‎ , ‎Operational matrix‎ , ‎B-Spline function‎ , ‎Collocation method