Secure Synchronization for Cyber-Physical Complex Networks Based on Self-Triggering Impulsive Control: Static and Dynamic Method

This paper investigates a self-triggered control scheme for a class of cyber-physical complex networks under deception attacks. The false data generated by attacks in both sensor-to-controller channels and controller-to-actuator channels are assumed to obey the Bernoulli distribution. By jointly combining distributed impulsive control scheme, time-varying impulsive effects and self-triggered strategy, a novel distributed self-triggered impulsive controller is elaborately designed. By integrating the definition of average impulsive gain, the contradiction analysis and Lyapunov stability theorem, sufficient conditions are derived for ensuring the secure synchronization within a given error bound. In addition, for further decreasing the triggering frequency and energy consumption, the advanced dynamic self-triggered criteria are obtained. It is worth mentioning that the updating laws adopted for dynamic self-triggered protocol in this paper is non-monotonic, which benefits to deal with the bounded synchronization. Finally, two numerical simulations are given to illustrate the feasibility of derived results.