Subspace Identification of Large-Scale 1D Homogeneous Networks

TL;DR

This paper introduces a novel subspace identification method for large-scale 1D homogeneous networks that relies solely on local input-output data, enabling efficient estimation of subsystem dynamics without full network knowledge.

Contribution

The paper presents a new subspace identification approach that uses local data and structural properties to identify subsystem models in large-scale homogeneous networks.

Findings

Effective identification demonstrated through simulation

Utilizes low-rank and Toeplitz structures in data matrices

Estimates local system matrices up to similarity transformations

Abstract

This paper considers the identification of large-scale 1D networks consisting of identical LTI dynamical systems. A new subspace identification method is developed that only uses local input-output information and does not rely on knowledge about the local state interaction. The identification of the local system matrices (up to a similarity transformation) is done via a low dimensional subspace retrieval step that enables the estimation of the Markov parameters of a locally lifted system. Using the estimated Markov parameters, the state-space realization of a single subsystem in the network is determined. The low dimensional subspace retrieval step exploits various key structural properties that are present in the data equation such as a low rank property and a {\em two-layer} Toeplitz structure in the data matrices constructed from products of the system matrices. For the estimation of the system matrices of a single subsystem, it is formulated as a structured low-rank matrix factorization problem. The effectiveness of the proposed identification method is demonstrated by a simulation example.