Secure synchronization of complex networks under deception attacks against vulnerable nodes

Secure synchronization for a class of nonlinearly coupled complex networks with deception attacks is investigated in this paper. False data caused by deception attacks is assumed to be injected into both the sensor-to-controller channels and the controller-to-actuator channels, which is modelled by Bernoulli stochastic variable. A distributed controller combined with impulsive protocol is applied for realizing the secure synchronization. By jointly applying the definition of average impulsive gain, the definition of average impulsive interval and the Lyapunov stability theorem, sufficient criteria are obtained to ensure the secure synchronization within the given error bound. In addition, pinning impulsive method is proposed to describe the attacks on vulnerable systems in complex networks, therefore, the theorem is extended to a less conservative situation. Finally, two numerical examples are presented to illustrate the effectiveness of theoretical results. (C) 2021 Elsevier Inc. All rights reserved.