Event-triggered adaptive dynamic programming for multi-player zero-sum games with unknown dynamics

In this paper, a novel event-triggered optimal control approach is developed to solve zero-sum game problems for continuous-time multi-player nonlinear systems with unknown dynamics. To begin with, a model neural network (NN) is employed to reconstruct the unknown multi-player nonlinear system by measured input and output data. Then, a critic NN is used to solve the event-triggered Hamilton–Jacobi–Isaacs (HJI) equation for multi-player zero-sum game. Meanwhile, the optimal control law and the worst disturbance law are approximated with the help of critic NN only, respectively. Compared with time-triggered method, the developed control law and the disturbance law are updated only when the triggering condition is violated; thus, the computational and communication burden are reduced. The Lyapunov stability analysis shows that the closed-loop system can be guaranteed to be stable. Finally, two simulation examples are provided to validate the effectiveness of the proposed method.