Reduced order modeling of linear consensus networks using weight assignments

This paper studies a model reduction method for linear consensus networks consisting of diffusively coupled single-integrators. For a given graph clustering of an original complex network, we construct a simplified network consisting of fewer nodes, where the edge weights are to be determined. An optimal weight assignment procedure is proposed to select suitable edge weights of the reduced network, aiming for the minimum mathcal{H}{2} approximation error between the original network and the reduced-order network model. The effectiveness of the proposed method is illustrated by means of an example.