A Numerical Method For Solving Fractional Optimal Control Problems Using The Operational Matrix Of Mott Polynomials

Abstract

‎This paper presents a numerical method for solving a class of fractional optimal control problems (FOCPs) based on numerical polynomial approximation‎. ‎The fractional derivative in the dynamic system is described in the Caputo sense‎. ‎We used the approach in order to approximate the state and control functions by the Mott polynomials (M-polynomials)‎. ‎We introduced the operational matrix of fractional Riemann-Liouville integration and apply it to approximate the fractional derivative of the basis‎. ‎We investigated the convergence of the new method and some examples are included to demonstrate the validity and applicability of the proposed method‎.