Identification of Large-Scale Vector-AutoRegressive models with Kronecker modeling

Baptiste Sinquin, Michel Verhaegen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

Abstract

In this work we address the identification of (2D) spatial-temporal dynamical systems described by the Vector-AutoRegressive (VAR) form. Modeling large-scale networks has been studied so far assuming different structures to alleviate the computational requirements, for example using sparsity in the interconnection pattern, [1]. A data-sparse structure has been investigated in [2] to model 1D strings of interconnected subsystems. The so-called Sequentially Semi-Separable (SSS) structure represents each of the subsystem in a 1D array with a mixed causal anti-causal linear time varying model which shares unknown interconnections with the closest neighbors. A data-sparse representation may not be achieved as the dimension grow as modeling multi-dimensional systems within the SSS framework requires an exponential number of parameters.
To overcome this curse of dimensionality, we present in this work a new class of
structured matrices to model 2D spatial-temporal systems. The class of Kronecker networks is first introduced and the identification of Vector Auto-Regressive models is subsequently addressed within this framework. Such a Kronecker structure leads to high data compression and benefits from the efficient linear algebra operations as described in [3]. The challenge lies in deriving algorithms that are, on the one hand, scalable in terms of data storage as well as in terms of computational complexity in identifying and using these models, e.g in subsequent control design, and on the other hand, that still ensures similar prediction performances compared to the unstructured least-squares estimates.
Original languageEnglish
Title of host publicationProceedings of the 2017 Symposium on Information Theory and Signal Processing in the Benelux
EditorsRichard Heusdens, Jos H. Weber
Pages202-203
ISBN (Electronic)978-94-6186-811-4
Publication statusPublished - 2017
Event2017 Symposium on Information Theory and Signal Processing in the Benelux: WIC/SP 2017 - Tu Delft Science Centre, Delft, Netherlands
Duration: 11 May 201712 Dec 2017
Conference number: 38
http://cas.tudelft.nl/sitb2017/

Conference

Conference2017 Symposium on Information Theory and Signal Processing in the Benelux
CountryNetherlands
CityDelft
Period11/05/1712/12/17
Internet address

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  • Research Output

    • 1 Dissertation (TU Delft)

    Structured matrices for predictive control of large and multi-dimensional systems

    Sinquin, B., 8 May 2019, 219 p.

    Research output: ThesisDissertation (TU Delft)

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    Cite this

    Sinquin, B., & Verhaegen, M. (2017). Identification of Large-Scale Vector-AutoRegressive models with Kronecker modeling. In R. Heusdens, & J. H. Weber (Eds.), Proceedings of the 2017 Symposium on Information Theory and Signal Processing in the Benelux (pp. 202-203)