Combination of epsilon and Ritz methods with multiscaling basis for solving a class of fractional optimal control problems

Abstract

This paper presents an approximate direct method for solving a class of fractional optimal control problems by combining the epsilon and Ritz methods and utilizing multiscaling basis functions. By applying the epsilon method, we transform the given optimal control problem into a variational problem. Then, we solve the variational problem approximately by the Ritz direct method with multiscaling polynomial basis functions. The choice of multiscaling basis functions provides a high rate of convergence for the Ritz method. The convergence of the derived approximate minimal to the exact one is extensively discussed. At the end some illustrative test examples are included to demonstrate the efficiency of the technique.