A Fermat polynomial method for solving optimal control problems

Abstract

In this paper, we propose an efficient computational approach to solve optimal control problems subject to state constraints and boundary conditions. The idea is to obtain an approximate numerical value of the objective function. The method is based on state parameterization. The state variable is considered as a linear combination of Fermat polynomials with unknown coefficients such that the state differential equations are satisfied. The optimal control problem is converted to quadratic programming problem which we easily solved by Lagrange method. Some numerical examples are considered to illustrate the reliability of the method. The numerical results obtained are accurate when compared with the analytic solution and results obtained from literatures.