Dynamic Leader-Follower Consensus with Adversaries: A Multi-Hop Relay Approach

This paper examines resilient dynamic leader-follower consensus within multi-agent systems, where agents share first-order or second-order dynamics. The aim is to develop distributed protocols enabling nonfaulty/normal followers to accurately track a dynamic/time-varying reference value of the leader while they may receive misinformation from adversarial neighbors. Our methodologies employ the mean subsequence reduced algorithm with agents engaging with neighbors using multi-hop communication. We accordingly derive a necessary and sufficient graph condition for our algorithms to succeed; also, our tracking error bounds are smaller than that of the existing method. Furthermore, it is emphasized that even when agents do not use relays, our condition is tighter than the sufficient conditions in the literature. With multi-hop relays, we can further obtain more relaxed graph requirements. Finally, we present numerical examples to verify the effectiveness of our algorithms.