Dynamic Leader-Follower Consensus with Adversaries: A Multi-Hop Relay Approach
Liwei Yuan, Hideaki Ishii
TL;DR
The paper addresses resilient dynamic leader-follower consensus in directed multi-agent systems with adversaries, proposing distributed MW-MSR-based protocols for first- and second-order dynamics to track a time-varying leader reference $x_d[k]$. It establishes a tight, necessary-and-sufficient graph condition: the normal network must be $(f+1)$-robust following with $l$ hops, with multi-hop relays enabling relaxation of connectivity requirements. The authors derive explicit finite-time consensus-error bounds $\overline{\epsilon}$ and demonstrate improved performance over existing static/dynamic-reference methods, including extensions to insecure leaders. Numerical simulations validate the theoretical results, showing robust tracking and formation control under Byzantine disturbances and across one- and two-dimensional scenarios.
Abstract
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.