Neural optimal tracking control of constrained nonaffine systems with a wastewater treatment application

In this paper, we aim to solve the optimal tracking control problem for a class of nonaffine discrete-time systems with actuator saturation. First, a data-based neural identifier is constructed to learn the unknown system dynamics. Then, according to the expression of the trained neural identifier, we can obtain the steady control corresponding to the reference trajectory. Next, by involving the iterative dual heuristic dynamic programming algorithm, the new costate function and the tracking control law are developed. Two other neural networks are used to estimate the costate function and approximate the tracking control law. Considering approximation errors of neural networks, the stability analysis of the proposed algorithm for the specific systems is provided by introducing the Lyapunov approach. Finally, via conducting simulation and comparison, the superiority of the developed optimal tracking method is confirmed. Moreover, the trajectory tracking performance of the wastewater treatment application is also involved for further verifying the proposed approach.