Event-Triggered Optimal Parallel Tracking Control for Discrete-Time Nonlinear Systems

A novel event-triggered optimal tracking control (ETOTC) method is developed for discrete-time nonlinear systems in this study. For the time-invariant desired trajectory, we prove that the tracking error is asymptotically stable, and an upper bound of the real performance index can be predetermined by a design parameter. For the time-varying desired trajectory, the developed triggering condition reduces communication costs by relaxing the restriction of the asymptotic stability of the closed-loop system, and we prove that the tracking error is uniformly ultimately bounded (UUB). The developed ETOTC method entails obtaining the next state of the real system. Therefore, a parallel control approach is proposed to predict the next state by constructing a parallel system for the real system. Neural networks (NNs) and adaptive dynamic programming (ADP) techniques are utilized in the parallel control approach. Moreover, the stability analysis of the closed-loop system is shown, and the tracking error and NN weight estimation errors are proved to be UUB using the Lyapunov approach. Finally, we validate the developed ETOTC method through two simulations.