Designing Fully Distributed Consensus Protocols for Linear Multi-Agent Systems With Directed Graphs

TLDR

Existing consensus protocols rely on global Laplacian eigenvalue information, which is not locally available. This work seeks to design a fully distributed adaptive consensus protocol for linear multi‑agent systems with directed communication graphs, enabling leader‑follower consensus whenever the graph contains a directed spanning tree rooted at the leader. The protocol is built solely from local agent dynamics and neighboring relative states, and the design is extended to accommodate multiple leaders. The resulting protocol operates without any global graph information, achieving fully distributed leader‑follower consensus.

Abstract

This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this paper, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.