Two Models of Latent Consensus in Multi-Agent Systems
For researchers in multi-agent coordination, this work offers theoretical extensions to consensus protocols under weak connectivity, but the contribution is incremental as it builds on established Laplacian-based methods.
The paper proposes first- and second-order consensus protocols for multi-agent systems, providing explicit asymptotic state representations using Laplacian eigenprojections. It introduces regularization models (dummy hub and weak background links) to handle dependency digraphs lacking a converging tree.
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.