Optimal Tracking Control Scheme for Discrete-Time Nonlinear Systems with Approximation Errors

Abstract

In this paper, we aim to solve an infinite-time optimal tracking control problem for a class of discrete-time nonlinear systems using iterative adaptive dynamic programming (ADP) algorithm. When the iterative tracking control law and the iterative performance index function in each iteration cannot be accurately obtained, a new convergence analysis method is developed to obtain the convergence conditions of the iterative ADP algorithm according to the properties of the finite approximation errors. If the convergence conditions are satisfied, it is shown that the iterative performance index functions converge to a finite neighborhood of the greatest lower bound of all performance index functions under some mild assumptions. Neural networks are used to approximate the performance index function and compute the optimal tracking control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, a simulation example is given to illustrate the performance of the present method.