Consensus of second-order multi-agent systems in the presence of locally bounded faults

We propose an algorithm for consensus of second-order sampled-data multi-agent systems in the presence of misbehaving agents. Each normal agent updates its states following a predetermined control law based on local information while some malicious agents make updates arbitrarily. The normal agents do not know the global topology of the network, but have prior knowledge on the maximum number of malicious agents in their neighborhood. Under the assumption that the network has sufficient connectivity in terms of robustness, we develop a resilient algorithm where each agent ignores the neighbors which have large and small position values to avoid being influenced by malicious agents.