Resiliency against malicious agents in maximum-based consensus

In this paper, we develop distributed algorithms for achieving resilient consensus via the maximum value-based approach when adversarial agents may be present in the network. The adversaries intend to prevent the nonfaulty, normal agents from reaching consensus. We extend the class of resilient methods known as the mean subsequence reduced (MSR) algorithms, where the agents make selections on their neighbours' information at the time of their updates so as to reduce the influence of the malicious agents. In particular, the normal agents try to arrive at the maximum value of their initial states. Due to the malicious agents, the exact maximum may not be reached, the advantage of the approach is the finite-time convergence. We present both synchronous and asynchronous versions of the update schemes and characterize graph theoretic conditions for achieving resilient consensus. A numerical example is provided to illustrate our results.