Cluster Assignment in Multi-Agent Systems

TL;DR

This paper presents a method for designing directed graphs in multi-agent systems that guarantees convergence to a specified cluster configuration by leveraging automorphism group actions.

Contribution

It introduces a graph design approach ensuring prescribed clustering in homogeneous diffusive networks using automorphism group orbits.

Findings

Established bounds on the number of edges needed for graph construction

Provided a constructive method for designing such graphs

Supported results with numerical examples

Abstract

We study cluster assignment in multi-agent networks. We consider homogeneous diffusive networks, and focus on design of the graph that ensures the system will converge to a prescribed cluster configuration, i.e., specifying the number of clusters and agents within each cluster. Leveraging recent results from cluster synthesis, we show that it is possible to design an oriented graph such that the action of the automorphism group of the graph has orbits of predetermined sizes, guaranteeing that the network will converge to the prescribed cluster configuration. We provide upper and lower bounds on the number of edges that are needed to construct these graphs along with a constructive approach for generating these graphs. We support our analysis with some numerical examples.