Kronecker-ARX models in identifying (2D) spatial-temporal systems

Conference paper (2017)

Authors

B. Sinquin Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
M.H.G. Verhaegen Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
Research Group
Team Raf Van de Plas (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2017 B. Sinquin, M.H.G. Verhaegen
DOI: https://doi.org/10.1016/j.ifacol.2017.08.1855
Kronecker product Low-rank approximation 2D large-scale systems Vector AutoRegressive model
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Published Date

2017

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Raf Van de Plas

Abstract

In this paper we address the identification of (2D) spatial-temporal dynamical systems governed by the Vector Auto-Regressive (VAR) form. The coefficient-matrices of the VAR model are parametrized as sums of Kronecker products. When the number of terms in the sum is small compared to the size of the matrix, such a Kronecker representation leads to high data compression. Estimating in least-squares sense the coefficient-matrices gives rise to a bilinear estimation problem, which is tackled using a three-stage algorithm. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable performances with the unstructured least-squares estimation of VAR models. However, the number of parameters in the new modeling paradigm grows linearly w.r.t. the number of nodes in the 2D sensor network instead of quadratically in the full unstructured matrix case.