Approximate Optimal Tracking Control for a Class of Discrete-time Nonlinear Systems based on GDHP Iterative Algorithm

In this paper, an iterative globalized dual heuristic programming (GDHP) method is applied to optimal tracking control of a class of discrete affine nonlinear systems. In order to further consider the control signal in the varying process, this paper adds a control error difference term to the quadratic cost function. Through system transformation, the optimal tracking problem is transformed into designing the optimal regulator problem for tracking error dynamics. Then, the GDHP algorithm is introduced to deal with the optimal regulation problem. Three neural networks are used as parameter structures to realize the algorithm, which aims at approximating cost function, control law and error dynamics respectively. A simulation example is given to verify the effectiveness of the method.