Model reduction of networked passive systems through clustering

TL;DR

This paper introduces a clustering-based model reduction method for networked passive systems that preserves synchronization and offers a physically interpretable reduced model.

Contribution

It proposes a novel clustering approach based on controllability and observability analysis for reducing networked passive systems, maintaining synchronization.

Findings

Reduced-order networked system with preserved synchronization

Clustering based on controllability and observability analysis

Illustrated with a practical example

Abstract

In this paper, a model reduction procedure for a network of interconnected identical passive subsystems is presented. Here, rather than performing model reduction on the subsystems, adjacent subsystems are clustered, leading to a reduced-order networked system that allows for a convenient physical interpretation. The identification of the subsystems to be clustered is performed through controllability and observability analysis of an associated edge system and it is shown that the property of synchronization (i.e., the convergence of trajectories of the subsystems to each other) is preserved during reduction. The results are illustrated by means of an example.