Online optimal regulation and tracking control of nonlinear discrete-time system with control constraints

In this paper, an online adaptive dynamic programming (ADP) scheme is proposed to obtain the optimal control of discrete-time nonlinear system with input constraints. First, a control performance function is used to reflect the input constraints, then the neural-network-based ADP scheme is presented, in which one neural network (NN) is designed to approximate the performance function and the other one to compute the constrained optimal control. This online method does not need the knowledge of internal system dynamics and off-line computation. Meanwhile, the proposed method is also extended to the optimal tracking control for certain nonlinear system. Further, stability of the closed loop system is demonstrated by the Lyapunov method. Finally, simulation examples are given to show the effectiveness of the proposed method.