A new optimal control method for discrete-time nonlinear systems with approximation error

In this paper, a new optimal control method is proposed for discrete-time nonlinear systems based on iterative adaptive dynamic programming (ADP) algorithm with approximation error. In each iteration of the proposed algorithm, the iterative control law and iterative performance index function cannot be accurately obtained. The convergence conditions of the iterative ADP algorithm are presented. According to the convergence conditions, the iterative performance index functions are proved to be convergent to a small neighborhood of the optimal performance index function. Finally, a simulation example is given to illustrate the performance of the proposed method.