Event-Triggered ADP for Multi-Player Zero-Sum Game of Partially Unknown Nonlinear System with Constraints on Dead Zone Inputs

This article proposes a class of multi-player zero-sum (ZS) game solutions on partially unknown continuous-time nonlinear systems possessing dead zone input constraints. Firstly, in the control design, control inputs and dead zones are chosen as the players on both sides of the game. Subsequently, an adaptive dynamic programming (ADP) based event-triggered control (ETC) is developed. The system dynamics which are unknown can be approximated using an identifier neural network (NN), and a critic NN is utilized to estimate the optimal value function. The states are sampled and the weights of NN are updated when the event-triggering condition is satisfied. For time-triggered methods, the developed approach greatly reduces the complexity of computation and the Zeno behavior is avoided through proof. The system states and errors of NN weights using Lyapunov stability theory are shown as uniformly ultimately bounded (UUB). Finally, the validity of the ADP-based ETC program is verified by simulation.