The Iterative Method for Optimal Control Problems by the Shifted Legendre Polynomials

Abstract

In this paper an iterative method based on shifted Legendre polynomials is presented to obtain the approximate solutions of optimal control problems subject to integral equations. The operational matrices of integration and product of shifted Legendre polynomials for solving integral equation is employed. The methodology is based on the parametrization of control and state functions. This converted the problem to nonlinear optimization problem in any iteration. In addition, some numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.