Event-Triggered Approximate Byzantine Consensus With Multi-Hop Communication

In this article, we consider a resilient consensus problem for the multi-agent network where some of the agents are subject to Byzantine attacks and may transmit erroneous state values to their neighbors. In particular, we develop two event-triggered update schemes to tackle this problem as well as reduce the communication for each agent. Our approach is based on the mean subsequence reduced (MSR) algorithm with agents being capable to communicate with multi-hop neighbors through relaying process. Since communication delays are critical in such an environment, we provide necessary graph conditions for the proposed algorithms to perform well with delays in the communication. Moreover, a novel multi-hop relay scheme with event-triggered feature is proposed. It can reduce more transmissions than the conventional one-hop event-triggered algorithm. We also highlight that through multi-hop communication, the network connectivity can be reduced especially in comparison with the common one-hop communication case. Lastly, we show the effectiveness of the proposed algorithms by numerical examples.