Numerical solution of nonlinear optimal control problems based on state parametrization

Document Type : Regular Paper


1 Faculty of Mathematics, Yazd University, Yazd, P.O. Box 89197/741, Iran

2 Faculty of Advanced Education, Islamic Azad University, Yazd Branch, Yazd, P.O.Box 89195/155, Iran


In this paper, solution of nonlinear optimal control problems and the controlled Duffing oscillator, as a special class of optimal control problems, are considered and an efficient algorithm is proposed. This algorithm is based on state parametrization as a polynomial with unknown coefficients. By this method, the control and state variables can be approximated as a function of time. Also, the numerical value of the performance index is obtained readily. The convergence of the algorithm is proved. To demonstrate reliability and efficiency of the proposed algorithm, the scheme is tested on some numerical examples.