Stable iterative optimal control for discrete-time nonlinear systems using numerical controller

This paper is concerned with a new iterative adaptive dynamic programming (ADP) algorithm to solve optimal control problems for infinite horizon discrete-time nonlinear systems using a numerical controller. The convergence conditions of the iterative ADP are developed considering the errors by the numerical controller which show that the iterative performance index functions can converge to the greatest lower bound of all performance indices within a finite error bound. Neural networks and digital computer are used to approximate the iterative performance index function and compute the numerically iterative 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.