Clustering-Based Model Reduction of Laplacian Dynamics With Weakly Connected Topology

Abstract

This article studies the structure-preserving model reduction of Laplacian dynamics, which represent weakly connected directed networks with diffusive couplings. The notion of clusterability is introduced to guarantee a bounded reduction error, and a clustering algorithm is then proposed to partition the nodes into clusters, such that the nodes in each cluster form a connected subgraph of the original network. Then, a reduced-order model, which is established using the generalized balanced form of the original network, preserves the weakly connection structure and consensus property. Finally, the effectiveness of the proposed approach is illustrated by a numerical example.