Resilient Impulsive Control for Second-Order Consensus under Malicious Nodes

In this brief, we investigate the problem of resilient consensus in continuous-time second-order networks, where some nodes might be faulty or adversarial. Despite the existence of such malicious and unexpected behaviors, the normal agents still aim to reach an agreement. Towards this end, a resilient impulsive algorithm is proposed, in which the signal transmission among agents occurs with aperiodic intervals. At each sampling time, the normal agent removes the most extreme values in the neighborhood and then derives its control signal with the remaining ones. We show the influence of the malicious nodes on the normal ones would be limited by this manner. Sufficient conditions related to the network topology and tolerable number of misbehaving nodes are finally established to achieve the resilient consensus.