Adaptive Neural Event-Triggered Output-Feedback Optimal Tracking Control for Discrete-Time Pure-Feedback Nonlinear Systems

In this article, a novel event-triggered (ET) output-feedback optimal tracking control scheme is developed for a class of uncertain discrete-time nonlinear systems in the pure-feedback form with immeasurable states. Firstly, different from the traditional n-step-ahead input-output prediction model, the immeasurable states of the system are estimated in real time by designing a neural network (NN) state observer. Then, the implicit function theorem and the mean value theorem are combined to tackle the nonaffine terms. The variable substitution approach is applied to overcome the causal contradiction problem during the backstepping design, and meanwhile the n-step time delays caused by the traditional nstep-ahead prediction model are avoided. Subsequently, the critic NN and the action NN are employed to minimize the system long-term performance measure. Under the adaptive critic design framework, an optimal controller is designed to obtain the optimal control performance. Furthermore, an ET mechanism is embedded between sensors and controllers to reduce network burden. A novel ET condition is developed to save network resources and guarantee the desired tracking control performance. According to the Lyapunov stability analysis, all the closed-loop system signals are guaranteed to be uniformly ultimately bounded.