Synchronization of Resilient Complex Networks Under Attacks

One fundamental yet challenging issue in security control for resilient complex networks is to construct distributed control laws for the networks to perform various cooperative tasks in the presence of failures and attacks, where resilient indicates that the complex networks are exposed to the environment with cyber uncertainties and malicious adversaries. This is particularly important in today’s critical infrastructure networks since most of them are vulnerable to attacks in the era of the Internet. Inspired by this observation, this paper focuses on synchronization control for resilient complex networks subject to cyber and physical attacks, where the states of nodes being attacked may change abruptly (i.e., the synchronization error may suffer impulsive disturbances), and some nodes as well as their corresponding connections may not work in some instances. Suppose that a smart control center is equipped in the considered network to detect the attacks in real time. Furthermore, the nodes and communication channels are assumed to be recovered through some repair work after detecting the attacks. On the theoretical side, by using the ${M}$ -matrix theory, we get a few sufficient criteria to guarantee the achievement of secure synchronization against attacks on both nodes and communication links. On the algorithmic side, security control algorithm and architecture are proposed to select the coupling strength and the feedback gain matrix to realize synchronization. Finally, we perform two simulation examples to validate our theoretical results.