Model Reduction of Multiagent Systems Using Dissimilarity-Based Clustering

This technical note investigates a model reduction scheme for large-scale multiagent systems. The studied system is composed of identical linear subsystems interconnected by undirected weighted networks. To reduce the network complexity, a notion of nodal dissimilarity is established on the $\mathcal {H}_2$-norms of transfer function deviations, and a new graph clustering algorithm is proposed to aggregate the pairs of nodes with smaller dissimilarities. The simplified system is verified to preserve an interconnection structure and the synchronization property. Moreover, a computable bound of the approximation error between the full-order and reduced-order models is provided, and the feasibility of the proposed approach is demonstrated by network examples.