Solution of a Class of Fractional Optimal Control Problems using Spectral Bernstein Method and Operational Matrix

In this paper, we apply the spectral Ritz method to solve a class of fractional optimal control problems (FOCPs). The Bernstein polynomials along with fractional operational derivative matrix is used to estimate the unknown state and control functions. The method is reliable because of its computationally consistency and having a good flexibility in the sense of satisfying the initial-boundary conditions. Meanwhile, a new fractional operational matrix usable in the Ritz method is formed. Finally, by substituting the estimated functions into the cost function, an unconstrained nonlinear optimization problem is achieved. To solve this optimization problem, the Matlab 2012 software and its optimization toolbox is used. At last, some illustrative test problems are added to show the applicability of the new method.