Exponential Synchronization of Infinite-Dimensional Stochastic Systems with Poisson Jumps Under Aperiodically Intermittent Impulse Control

A novel aperiodically intermittent impulse control (AIIC) method is proposed to investigate the exponential synchronization in mean square (ESMS) of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps (ISIDSP). The AIIC control strategy inherits the flexibility of aperiodically intermittent control, including the variable control period, adjustable control interval length, and the discretization of impulsive control. In addition, this article introduces a novel mild Itô's formula. By leveraging semigroup theory, the contraction mapping principle, and graph theory, along with constructing the Lyapunov function, the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established. Furthermore, the mean-square exponential synchronization problem of the above systems is resolved, and the constraints within the mild solution domain are alleviated. These criteria clarify the impact of control parameters, control intervals and network topology on ESMS. The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes, and the validity of the results is verified using numerical simulations.