Asymptotic properties of subspace estimators

Bauer, Dietmar

doi:10.1016/j.automatica.2004.11.012

Cited by 91 publications

(62 citation statements)

References 35 publications

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“…Along this line, it is of interest to extend the nonparametric paradigm to the design of optimal predictors. By the way, predictor estimation, beyond being of interest on its own, is the preliminary step of subspace identification methods [9], [10], [11], [12]. Therefore, improving predictor design may enhance performance of subspace identification methods as well.…”

Section: Introductionmentioning

confidence: 99%

Predictor estimation via Gaussian regression

Pillonetto

Chiuso²,

Nicolao

2008

2008 47th IEEE Conference on Decision and Control

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Abstract-A novel nonparametric paradigm to model identification has been recently proposed where, in place of postulating finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinitedimensional space. In this paper, we extend such nonparametric approach to the design of optimal predictors by interpreting the predictor coefficients as realizations of Gaussian processes. Numerical experiments, where data are generated by ARMAX models, are used to show advantages of the new approach in terms of both predictive capability on new data and accuracy in reconstruction of predictor coefficients. In a companion paper, it is also shown how this new approach to predictor design may greatly enhance performance of subspace identification methods.

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Section: Introductionmentioning

confidence: 99%

Predictor estimation via Gaussian regression

Pillonetto

Chiuso²,

Nicolao

2008

2008 47th IEEE Conference on Decision and Control

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“…In parallel, a large number of subspace identification methods (SIM) have been developed since the 90's (see e.g. (Verhaegen, 1994;Van Overschee and De Moor, 1996) and (Viberg, 1995;Bauer, 2005) for relevant overviews). One of the reasons for the success of SIM lies in the direct correspondence between geometric operations on matrices constructed from input/output data and their implementation in terms of well known, stable and reliable algorithms from the field of numerical linear algebra.…”

Section: Introductionmentioning

confidence: 99%

Subspace-Based Optimal Iv Method for Closed-Loop System Identification

Gilson

Mercère

2006

IFAC Proceedings Volumes

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This paper deals with an optimal instrumental variable method dedicated to subspace-based closed-loop system identification. The presented solution is based on the MOESP technique but requires to modify the original scheme by proposing a new PO MOESP method which uses reconstructed past input and past output data as instrumental variables. The developed approach is then illustrated via a simulation example and a comparison with other subspace-based methods.

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“…The latter problem has been studied extensively in the literature and numerous algorithms exist to solve it [22,14,20,21,2]. This means that using any of these algorithms 9 solves the problem of determining the matrices A, B, C, D.…”

Section: Identification Of the Matrices A B C Dmentioning

confidence: 99%

“…This is a linear identification problem that has been studied extensively in the literature, see for example [22,14,20,21,2] and references therein. Let M be some identification algorithm that allows the determination of the unknown matrices of the linear system, using some appropriate identification input ϑ.…”

Section: Second Stage: Identification Of the Matrices A B C Dmentioning

confidence: 99%

A Unified Approach for the Identification of SISO/MIMO Wiener and Hammerstein Systems*

Ikhouane

Giri

2012

IFAC Proceedings Volumes

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Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N-L and L-N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a unified framework for the identification of these systems that is valid for SISO and MIMO systems, discrete and continuous-time setting, and with the only a priori knowledge that the system is either Wiener or Hammerstein.

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Asymptotic properties of subspace estimators

Cited by 91 publications

References 35 publications

Predictor estimation via Gaussian regression

Predictor estimation via Gaussian regression

Subspace-Based Optimal Iv Method for Closed-Loop System Identification

A Unified Approach for the Identification of SISO/MIMO Wiener and Hammerstein Systems*

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