Bipartite secure synchronization for dynamic networks under deception attacks via delay-dependent impulsive control

Abstract

In this paper, we investigate mean-square bounded bipartite synchronization of coupled dynamic networks subject to deception attacks, especially under directed/undirected signed interconnection structures. An impulsive secure control input involving stabilizing delays is proposed. The average impulsive delay (AID) method is used to fetch the information of time delay existing in impulses, and then this information is effectively integrated to mitigate the negative effects of deception attacks on synchronization. A concept of stochastic variables is introduced to serve as a measure of attack success when delayed impulsive control signals are replaced with false data from the impulsive controller-to-actuator. To achieve desired synchronization performance under deception attacks, the gains of pinning impulsive control, the average impulsive interval (AII), AID and the attack intensity are co-designed. An upper bound for synchronization errors is provided, which can be adjusted with multiple adjustable parameters. In addition, the AII and AID methods are used to remove the restriction on upper/lower bounds of two consecutive impulsive instants. Finally, numerical examples are given to illustrate the validity of the theoretical results.