In this paper,we aim to solve the finite horizon optimal control problem for a class of discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming(ADP) approach.A new-optimal control algorithm based on the iterative ADP approach is proposed which makes the performance index function converge iteratively to the greatest lower bound of all performance indices within an error according to within finite time.The optimal number of control steps can also be obtained by the proposed-optimal control algorithm for the situation where the initial state of the system is unfixed.Neural networks are used to approximate the performance index function and compute the optimal control policy,respectively,for facilitating the implementation of the-optimal control algorithm.Finally,a simulation example is given to show the results of the proposed method.
