Secure synchronization of stochastic complex networks subject to deception attack with nonidentical nodes and internal disturbance

This paper aims at exploring the mean-square bounded synchronization of clustered stochastic systems under deception attack which is a ubiquitous phenomenon in cyber-physical network. Actually, when controllers in network send controlling signal to physical plants, controller-to-actuator channel may be injected with wrong signal by malicious hackers intending to destroy the system’s performance. To describe attacker’s behavior, some random variables are introduced to describe whether the cluster’s channel is attacked or not in the controlled moment. Meanwhile, it has been proved that pinning impulsive control is effective to offset both stochastic effect and attack effect, where the nodes with bigger error will be chosen to be pinned in impulsive instants. By applying Gronwall-Bellman inequality and Lyapunov method on stochastic network, several kinds of mean-square bounded synchronization criteria based on pinning impulsive strategy are derived in terms of algebraic conditions and some reasonable assumptions. Finally, some numerical simulations are presented to illustrate the effectiveness of the theoretical results in this paper.