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

TL;DR

This paper introduces a novel method for reducing the complexity of consensus network systems by optimizing edge weights and nodal time-scales to minimize approximation errors, enhancing efficiency while preserving essential dynamics.

Contribution

It presents a new model reduction technique that optimizes edge weights and nodal time-scales using H-infinity and H-2 criteria for consensus networks based on graph clustering.

Findings

Optimized parameters significantly reduce approximation errors.

H-infinity and H-2 methods effectively improve model accuracy.

Numerical example demonstrates practical effectiveness.

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.