Legendre Approximations for Solving Optimal Control Problems Governed by Ordinary Differential Equations

In this paper Legendre integral method is proposed to solve optimal control problems governed by higher order ordinary differential equations. Legendre approximation method reduced the problem to a constrained optimization problem. Penalty partial quadratic interpolation method is presented to solve the resulting constrained optimization problem. Error estimates for the Legendre approximations are derived and a technique that gives an optimal approximation of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method.