In order to obtain the optimal control strategy of nonlinear discrete-time systems, based on the principle of
adaptive dynamic programming, an adaptive dynamic programming method with error bound is proposed. For any arbitrary
state, a length-limited control sequence is used to approximate the optimal control sequence, which makes the error between
the performance index and optimal performance index in a smaller range. A nonlinear discrete-time system is chosen for the
numerical experiments about the performance of algorithm, and the results show the effectiveness of the algorithm, and a
near optimal control strategy is obtained with less computational cost.