Optimal control for discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming

A new ε-optimal control algorithm based on the adaptive dynamic programming (ADP) is proposed to solve the finite horizon optimal control problem for a class of discrete-time nonlinear systems with unfixed initial state. The proposed algorithm makes the performance index function converges iteratively to the greatest lower bound of all performance indices within an error bound according to ε with finite time. The number of optimal control steps can also be obtained by the proposed ADP approach for the situation when the initial state of the system is unfixed. A simulation example is given to show the performance of the present method.