Two Models of Latent Consensus in Multi-Agent Systems

TL;DR

This paper introduces new consensus protocols for multi-agent systems, providing explicit asymptotic state representations and analyzing models with weak influence structures, including a dummy agent and background links.

Contribution

It presents novel first and second-order consensus protocols with explicit asymptotic state formulas, especially for systems lacking a converging spanning tree.

Findings

Explicit asymptotic state representations involving eigenprojections of the Laplacian.

Regularization models with dummy agents or background links enable coordination.

Analysis of classical second-order consensus protocol asymptotics.

Abstract

In this paper, we propose several consensus protocols of the first and second order for networked multi-agent systems and provide explicit representations for their asymptotic states. These representations involve the eigenprojection of the Laplacian matrix of the dependency digraph. In particular, we study regularization models for the problem of coordination when the dependency digraph does not contain a converging tree. In such models of the first kind, the system is supplemented by a dummy agent, a "hub" that uniformly, but very weakly influences the agents and, in turn, depends on them. In the models of the second kind, we assume the presence of very weak background links between the agents. Besides that, we present a description of the asymptotics of the classical second-order consensus protocol.