Secure impulsive cluster synchronization control of complex dynamical networks with parameter mismatches under deception attacks

The issue of secure cluster synchronization (SCS) of complex dynamical networks (CDNs) with parameter mismatches under deception attacks is investigated in this article. Firstly, the deception attacks are supposed to inject false information into controller-to-actuator channels, while the occurrences of deception attack are always subject to Bernoulli distribution. Secondly, an improved pinning impulsive control strategy is designed. The impulsive gain in the control strategy is take from a new range. Moreover, we obtain the estimation of synchronization error upper bound and boundaries of secure synchronization region. The synchronization error will converge to a bounded ball that depends on attack energy at a exponential rate. The CDNs without deception attacks under pinning impulsive control can achieve complete cluster synchronization. Finally, two numerical examples with 20 nodes based on MATLAB software are presented to demonstrate the effectiveness of the theoretical results.