Model Reduction Methods for Complex Network Systems

TL;DR

This paper reviews reduction methods for complex network systems, focusing on simplifying both the network structure and node dynamics while maintaining key properties like stability and synchronization.

Contribution

It provides a comprehensive overview of topological and dynamical reduction techniques, including graph clustering, classical extensions, and a generalized balancing method.

Findings

Graph clustering effectively reduces network complexity.

Extensions of classical methods preserve stability during reduction.

A generalized balancing method simplifies structure and dynamics simultaneously.

Abstract

Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of interconnections may also be of high complexity. Therefore, it is relevant to study reduction methods for network systems. An overview on reduction methods for both the topological (interconnection) structure of the network and the dynamics of the nodes, while preserving structural properties of the network, and taking a control systems perspective, is provided. First topological complexity reduction methods based on graph clustering and aggregation are reviewed, producing a reduced-order network model. Second, reduction of the nodal dynamics is considered by using extensions of classical methods, while preserving the stability and synchronization properties. Finally, a structure-preserving generalized balancing method for simplifying simultaneously the topological structure and the order of the nodal dynamics is treated.