Consensus Problems in Networks of Agents under Nonlinear Protocols with Directed Interaction Topology

TL;DR

This paper extends the theoretical understanding of consensus in multi-agent networks by analyzing nonlinear protocols over directed graphs, showing that strong connectivity and increasing protocols ensure consensus.

Contribution

It generalizes previous results from undirected to directed graphs, establishing conditions for consensus with nonlinear protocols.

Findings

Strong connectivity in directed graphs guarantees consensus.

Strictly increasing nonlinear protocols lead to consensus.

Examples confirm the theoretical results.

Abstract

The purpose of this short paper is to provide a theoretical analysis for the consensus problem under nonlinear protocols. A main contribution of this work is to generalize the previous consensus problems under nonlinear protocols for networks with undirected graphs to directed graphs (information flow). Our theoretical result is that if the directed graph is strongly connected and the nonlinear protocol is strictly increasing, then consensus can be realized. Some simple examples are also provided to demonstrate the validity of our theoretical result.