Optimal learning control for discrete-time nonlinear systems using generalized policy iteration based adaptive dynamic programming

In this paper, a novel generalized policy iteration algorithm is investigated to solve infinite horizon optimal control problems for discrete-time nonlinear systems. Two iteration indices are introduced in the generalized policy iteration algorithm, which iterate for policy improvement and policy evaluation, respectively. For the first time the properties of monotonicity, convergence and admissibility for the generalized policy iteration algorithm are analyzed to guarantee that the iterative performance index function converges to the optimum and the iterative control law stabilizes the control system. Finally, numerical results are presented to illustrate the performance of the developed method.