Event-triggered optimal control of discrete-time nonlinear system with external disturbance

This article studies the event-triggered optimal control of discrete-time nonlinear system subject to external disturbance. To optimize the performance of nonlinear system, we define a nonlinear quadratic value function and then establish the corresponding Hamilton-Jocabl (HJ) equation. Based on the Bellman optimization principle, we design the optimal control policy and the worst disturbance policy from the HJ equation. In order to reduce the update frequency of the control policy and the disturbance policy, we introduce an event-triggered updating mechanism. Subsequently, an event-triggered condition is designed and the stability of the system is proved using the Lyapunov method. The neural network structure is developed to approximate the optimal value function, the optimal control policy and the worst disturbance policy, respectively. Finally, simulation result demonstrates the feasibility of the proposed method.