Event-triggered H∞ optimal control for continuous-time nonlinear systems using neurodynamic programming

Abstract

In this paper, we propose a novel event-triggered neurodynamic programming (NDP) method to tackle the continuous-time nonlinear systems H∞ optimal control problem. First, the H∞ optimal control problem is converted to a zero-sum (ZS) two-player differential game problem. Then, we derive a triggering condition for the ZS two-player differential game problem with an event-triggered control input. The event-triggered controller is updated only at the triggering instants where the triggering condition is violated. So the event-triggered control manner can significantly reduce the update frequency of the controller. Therefore, event-triggered control has been an effective technique in resolving problems with limited communication and computation resources and is considered as an alternative to the traditional time-triggered control. Furthermore, in order to implement event-triggered control manner, we employ an actor-critic-disturbance neural networks (NNs) framework to approximate the optimal control input policy, the optimal value function and the disturbance policy respectively. The Lyapunov function method is applied to study the stability of the event-triggered closed-loop system and the uniformly ultimately boundedness (UUB) of the NN’s weights vector. Furthermore, the Zeno behavior exclusion is proved. Finally, two simulation examples are given to verify the effectiveness of the proposed algorithm.