Optimal Fixed-Point Tracking Control for Discrete-Time Nonlinear Systems via ADP

Based on adaptive dynamic programming (ADP), the fixed-point tracking control problem is solved by a value iteration (Ⅵ) algorithm. First, a class of discrete-time (DT) nonlinear system with disturbance is considered. Second, the convergence of a Ⅵ algorithm is given. It is proven that the iterative cost function precisely converges to the optimal value, and the control input and disturbance input also converges to the optimal values. Third, a novel analysis pertaining to the range of the discount factor is presented, where the cost function serves as a Lyapunov function. Finally, neural networks (NNs) are employed to approximate the cost function, the control law, and the disturbance law. Simulation examples are given to illustrate the effective performance of the proposed method.