Reduced Order Modeling of Diffusively Coupled Network Systems: An Optimal Edge Weighting Approach

This article studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original large-scale network, we construct a quotient graph with less number of vertices, where the edge weights are parameters to be determined. The model of a reduced network is thereby obtained with parameterized system matrices, and then, an edge weighting procedure is devised, aiming to select an optimal set of edge weights to minimize the approximation error between the original and the reduced-order network models in terms of
$\mathcal {H}_{2}$
-norm. The effectiveness of the proposed method is illustrated by a numerical example.