Mean-square bounded synchronization of complex networks under deception attacks via pinning impulsive control

In this paper, the mean-square bounded synchronization problem for a class of complex cyber-physical networks under deception attacks is investigated. The deception attack often takes place between the controller and the actuator, in which the injection of false data may cause the actuator to malfunction, while the occurrence of deception attack is always subject to Bernoulli distribution. An improved pinning impulsive control scheme is designed such that the status of all components in networks can be consistent, and the nodes with a high probability of being attacked are preferentially controlled. By means of Lyapunov method, inequality technique and mathematical induction method, it is proved that the given scheme can realize the mean-square bounded synchronization of complex networks under deception attack. Moreover, the required synchronization time is controllable and computable. Then, some sufficient conditions for mean-square bounded synchronization, error bound, and the maximum convergence time are obtained. Finally, two simulation examples demonstrate the validity of the given theoretical results.