Subspace identification of 1D large-scale heterogeneous network

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 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.

Distributed Identification of Contracting and/or Monotone Network Dynamics

“…Previous work in networked system identification can be loosely categorized into two areas; the identification of a network topology [10], [11], [12], and the identification of a system's dynamics with known topology. In the latter category, almost all prior work has focused on the case where subsystems are linear time invariant (LTI) and described by state space models [8], [13], [14] or transfer functions (a.k.a. modules) [15], [16].…”

Distributed Identification of Contracting and/or Monotone Network Dynamics

“…Previous work in networked system identification can be loosely categorized into two areas; the identification of a network topology [17], [18], [19], and the identification of a system's dynamics with known topology. In the latter category, almost all prior work has focused on the case where subsystems are linear time invariant (LTI) and described by state space models [15], [20], [21] or transfer functions (a.k.a. modules) [22], [23].…”