A New Method of Multistage Optimal Homotopy Asymptotic Method for Solution of Fractional Optimal Control Problem

This paper deals with a recent approximate analytical approach of the multistage optimal homotopy asymptotic method (MOHAM) for fractional optimal control problems (FOCPs). In this paper, FOCPs are developed in terms of a conformable derivative operator (CDO) sense. It is validated that the right CDO appears naturally in the formulation even when the system dynamics are described with the left CDO only. The CDO is employed to enlarge the stability region of the dynamical systems of the optimal control problems (OCPs). The necessary and transversal conditions are achieved using a Hamiltonian technique. The results demonstrated that as the fractional-order solution derivative tends to integer-order 1, the formulations lead to integer-order system solutions. Numerical results and a comparison with the exact solution and other approximate analytical solutions in fractional order are given to validate the efficiency of the MOHAM. Some numerical examples are included to demonstrate the effectiveness and applicability of the new technique. 

Keywords: Approximate analytical solution, Convergence analysis, Conformable derivative operator, Fractional calculus, Fractional Hamiltonian approach, Fractional optimal control problems.