Approximate optimal control for a class of nonlinear discrete-time systems with saturating actuators

In this paper, we solve the approximate optimal control problem for a class of nonlinear discrete-time systems with saturating actuators via greedy iterative Heuristic Dynamic Programming (GI-HDP) algorithm. In order to deal with the saturating problem of actuators, a novel nonquadratic functional is developed. Based on the nonquadratic functional, the GI-HDP algorithm is introduced to obtain the optimal saturated controller with a rigorous convergence analysis. For facilitating the implementation of the iterative algorithm, three neural networks are used to approximate the value function, compute the optimal control policy and model the unknown plant, respectively. An example is given to demonstrate the validity of the proposed optimal control scheme.