Cluster Assignment in Multi-Agent Systems : Sparsity Bounds and Fault Tolerance

TL;DR

This paper presents a method for designing multi-agent network graphs that ensure convergence to desired cluster configurations, with bounds on edges and robustness to agent failures.

Contribution

It introduces a novel graph design approach linking symmetries to clustering, providing bounds and constructive methods for fault-tolerant cluster assignment.

Findings

Graph design guarantees convergence to specified clusters

Bounds on the number of edges for graph construction

Robustness of clustering under agent malfunction

Abstract

We study cluster assignment in homogeneous diffusive multi-agent networks. Given the number of clusters and agents within each cluster, we design the network graph ensuring the system will converge to the prescribed cluster configuration. Using recent results linking clustering and symmetries, we show that it is possible to design an oriented graph for which the action of the automorphism group of the graph has orbits of predetermined sizes, guaranteeing the network will converge to the prescribed cluster configuration. We provide bounds on the number of edges needed to construct these graphs along with a constructive approach for their generation. We also consider the robustness of the clustering process under agent malfunction.