Adaptive dynamic programming for finite-horizon optimal tracking control of a class of nonlinear systems

This paper deals with the finite-horizon optimal tracking control for a class of discrete-time nonlinear systems using the iterative adaptive dynamic programming (ADP) algorithm. First, the optimal tracking problem is converted into designing a finite-horizon optimal regulator for the tracking error dynamics. Then, with convergence analysis in terms of cost function and control law, the iterative ADP algorithm via heuristic dynamic programming (HDP) technique is introduced to obtain the finite-horizon optimal tracking controller which makes the cost function close to its optimal value within an ε-error bound. Moreover, three neural networks are used to implement the algorithm, which aims at approximating the cost function, the control law, and the error dynamics, respectively. At last, an example is included to demonstrate the effectiveness of the proposed approach.