The Optimal Control of Discrete-Time Delay Nonlinear System with Dual Heuristic Dynamic Programming

In this paper, an effective iterative algorithm is proposed to deal with the optimal control problem of a class of nonlinear discrete-time delay systems. We define a meaningful performance index function to removing the disturbance of time delay terms. The iterative Dual Heuristic Programming (DHP) algorithm is introduced to design the optimal controller. Three neural networks are chosen to facilitate the implementation of the algorithm, which approximate the performance index function, the optimal control policy and the nonlinear delay system, respectively. A simulation example is given to demonstrate the validity of the proposed optimal control approach. For time-variant delay, this iterative algorithm shows the improved performance compared with other methods.