An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems

In this paper, we discuss a class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and fractional derivatives. The necessary optimality conditions are derived and shown that the conditions are sufficient under certain assumptions. Additionally, we design a well-organized algorithm to obtain the numerical solution of the proposed problem by exercising Laguerre polynomials. The key motive associated with the present approach is to convert the concerned fractional optimal control problem to an equivalent standard quadratic programming problem with linear equality constraints. Given examples illustrate the computational technique of the method together with its efficiency and accuracy. Graphical representations are provided to analyze the performance of the state and control variables for distinct prescribed fractions.