Event-Triggered Optimal Control for Discrete-Time Multi-Player Non-Zero-Sum Games Using Parallel Control

Abstract This paper presents a novel event-triggered optimal control (ETOC) method for discrete-time (DT) multi-player non-zero-sum games (NZSGs). First, a novel event-triggered algorithm is developed for DT multi-player NZSGs based on the time-triggered optimal value functions. Therefore, the developed event-triggered algorithm only needs to solve the time-triggered Hamilton-Jacobi-Bellman (HJB) equations. Then, the asymptotic stability of the closed-loop system is proved. Additionally, we show that an upper bound for the sum of the actual performance indices of all the players can be determined in advance. A key step in the implementation of the developed event-triggered algorithm is to obtain the next state of the actual system, which is difficult to implement on the actual system. Thus, a parallel control method is utilized to predict the next state by constructing the parallel system for the actual system and obtain the optimal value functions. The method that combines the developed event-triggered algorithm and parallel control is called the event-triggered optimal parallel control (ETOPC) method. The neural network (NN) technique and the iterative adaptive dynamic programming (IADP) technique are employed in parallel control. Moreover, the control stability is shown further in the consideration of the NN weight approximation errors. Finally, two simulations justify the theoretical conjectures.