A Combination of Variational and Penalty Methods for Solving a Class of Fractional Optimal Control Problems

Abstract

This paper develops an approximate method, based on the combination of epsilon penalty and variational methods, for solving a class of multidimensional fractional optimal control problems. The fractional derivative is in the Caputo sense. In the presented method, utilizing the epsilon method, the given optimal control problem transforms into an unconstrained optimization problem; then, the equivalent variational equality is derived for the given unconstrained problem. The variational equality is approximately solved by applying a spectral method.