Impulsive synchronization control for dynamic networks subject to double deception attacks

This paper investigates the problem of secure synchronization for coupled dynamic networks subject to two types of deception attacks. Deception attacks are considered in both the controller-to-actuator and sensor-to-controller communication channels and modeled as Bernoulli distributions. The same and different attack probabilities of each node in dynamic networks are considered, respectively. A novel secure impulsive controller is introduced, mitigating malicious information from deception attacks and ensuring bounded synchronization. The average impulsive interval (AII) method is employed to relax the constraints on the upper and lower bounds of consecutive impulses, which is not adequately addressed by the previous secure impulsive control methods. Additionally, the paper establishes an upper bound for synchronization errors and proposes a method to design the AII based on attack probabilities. Finally, two numerical examples are provided to show the validity of our control approach.