Neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems with approximation errors

In this paper, a new infinite horizon neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems is developed. The idea is to use iterative adaptive dynamic programming (ADP) algorithm to obtain the iterative tracking control law which makes the iterative performance index function reach the optimum. When the iterative tracking control law and iterative performance index function in each iteration cannot be accurately obtained, the convergence criteria of the iterative ADP algorithm are established according to the properties with finite approximation errors. If the convergence conditions are satisfied, it shows that the iterative performance index functions can converge to a finite neighborhood of the lowest bound of all performance index functions. Properties of the finite approximation errors for the iterative ADP algorithm are also analyzed. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Convergence properties of the neural network weights are proven. Finally, simulation results are given to illustrate the performance of the developed method.