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

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. ${\mathcal{H}_\infty }$ - and ${\mathcal{H}_2}$-based optimization approaches are proposed to select the reduced network parameters such that the corresponding approximation errors, i.e., the ${\mathcal{H}_\infty }$- and ${\mathcal{H}_\infty }$-norms of the error system, are minimized. The effectiveness of the proposed model reduction methods is illustrated via a numerical example.