Model Reduction of Consensus Network Systems via Selection of Optimal Edge Weights and Nodal Time-Scales

Abstract: This paper proposes model reduction approaches for consensus network systems based on a given clustering of the underlying graph. Namely, given a consensus network system of time-scaled agents evolving over a weighted undirected graph and a graph clustering, a parameterized reduced consensus network system is constructed with its edge weights and nodal time-scales as the parameters to be optimized. H-infinity- and H-2-based optimization approaches are proposed to select the reduced network parameters such that the corresponding approximation errors, i.e., the H-infinity- and H-2-norms of the error system, are minimized. The effectiveness of the proposed model reduction methods is illustrated via a numerical example.