Asynchronous Approximate Byzantine Consensus via Multi-hop Communication

In this paper, we consider a multi-agent resilient consensus problem, where some of the agents try to prevent the normal ones from reaching consensus. Specifically, we study an approximate consensus problem for the class of Byzantine adversaries when agents update asynchronously and there are time delays in the agents' communication. Our approach is based on that of the socalled weighted mean subsequence reduced (W-MSR) algorithm with a special emphasis on its use in agents capable to communicate with multi-hop neighbors. We find a tight graph condition for the proposed multi-hop weighted MSR algorithm to solve the asynchronous approximate Byzantine consensus problem. The proposed algorithm is more light weighted compared to the conventional flooding-based algorithm. At the end, we also provide numerical examples to show the efficiency of the proposed algorithm.