Fuzzy reinforcement learning synchronization of stochastic dynamic networks: An adaptive event-triggered strategy

This study delves into the challenge of achieving optimal synchronization control for time-delayed stochastic dynamic networks through fuzzy reinforcement learning (FRL), underpinned by a novel event-triggered strategy. Traditionally, optimal control is determined by solving the Hamilton-Jacobi-Bellman (HJB) equation. However, the strong nonlinearity and uncertain dynamics inherent in such systems render the solution of the HJB equation particularly arduous. To address this problem, an adaptive FRL algorithm is formulated within an identifier-critic-actor framework, which is derived from the negative gradient of simple adaptive functions. This approach yields a relatively straightforward optimal synchronization controller that eliminates the need for the persistent excitation condition. Subsequently, fuzzy logic systems (FLSs) are designed to approximate unknown uncertainties. A dynamics-estimating identifier and critic/actor FLSs are designed for performance evaluation and control signal generation, respectively. Moreover, a dynamic event-triggered optimal control (DETOC) is proposed. In this strategy, the triggering threshold is adaptively adjusted in real time, effectively reducing communication overhead and computational load. Notably, the optimal control policy is directly approximated by the FRL, bypassing the need to solve the HJB equation. Specifically, the value function is approximated by the critic FLSs for performance evaluation, while the control signal is directly generated by the actor FLSs based on the current system state. Finally, within the FRL-driven DETOC mechanism, the developed control method ensures that all synchronization error signals remain bounded. Its effectiveness is thoroughly verified and demonstrated through simulation examples.