Iterative GDHP-based approximate optimal tracking control for a class of discrete-time nonlinear systems

In this paper, an iterative globalized dual heuristic programming (GDHP) method is developed to deal with the approximate optimal tracking control for a class of discrete-time nonlinear systems. The optimal tracking control problem is formulated by solving the discrete-time Hamilton-Jacobi-Bellman (DTHJB) equation. Then, it is approximately solved by the developed iterative GDHP-based algorithm with convergence analysis. The iterative GDHP algorithm is implemented by constructing three neural networks to approximate the error system dynamics, the cost function with its derivative, and the control policy in each iteration, respectively. The information of the cost function and its derivative is provided during iteration calculation. Two simulation examples are investigated to verify the performance of the proposed approximate optimal tracking control approach.