A new interpretation of subspace methods by using Schur complement

Yoshinori Takei; Jun Imai; Kiyoshi Wada

A new interpretation of subspace methods by using Schur complement

Yoshinori Takei, Jun Imai, Kiyoshi Wada

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper, we present a new interpretation of the subspace-based state space system identification (4SID) method by using a subspace extraction via Schur complement (SES). Several efficient implementations of subspace-based identification methods (e.g., N4SID, etc) have been thus far developed and proposed. We consider the MIMO output error state space model identification, the so-called MOESP. Making a comparison between the matrix obtained by the QR factorization in the MOESP and the Schur complement matrix of data product moments shows that the estimate of the extended observability matrix can be obtained by using the SES procedure. Viewing that fact that the Schur complement yielded by the subspace extraction coincides with the error covariance in the least squares (LS), our interpretation will pave the way for the derivation of the recursive algorithm of the 4SID method.

Original language	English
Pages (from-to)	3924-3929
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	4
Publication status	Published - Dec 1 2001
Externally published	Yes
Event	40th IEEE Conference on Decision and Control (CDC) - Orlando, FL, United States Duration: Dec 4 2001 → Dec 7 2001

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

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title = "A new interpretation of subspace methods by using Schur complement",

abstract = "In this paper, we present a new interpretation of the subspace-based state space system identification (4SID) method by using a subspace extraction via Schur complement (SES). Several efficient implementations of subspace-based identification methods (e.g., N4SID, etc) have been thus far developed and proposed. We consider the MIMO output error state space model identification, the so-called MOESP. Making a comparison between the matrix obtained by the QR factorization in the MOESP and the Schur complement matrix of data product moments shows that the estimate of the extended observability matrix can be obtained by using the SES procedure. Viewing that fact that the Schur complement yielded by the subspace extraction coincides with the error covariance in the least squares (LS), our interpretation will pave the way for the derivation of the recursive algorithm of the 4SID method.",

author = "Yoshinori Takei and Jun Imai and Kiyoshi Wada",

year = "2001",

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language = "English",

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journal = "Proceedings of the IEEE Conference on Decision and Control",

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note = "40th IEEE Conference on Decision and Control (CDC) ; Conference date: 04-12-2001 Through 07-12-2001",

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T1 - A new interpretation of subspace methods by using Schur complement

AU - Takei, Yoshinori

AU - Imai, Jun

AU - Wada, Kiyoshi

PY - 2001/12/1

Y1 - 2001/12/1

N2 - In this paper, we present a new interpretation of the subspace-based state space system identification (4SID) method by using a subspace extraction via Schur complement (SES). Several efficient implementations of subspace-based identification methods (e.g., N4SID, etc) have been thus far developed and proposed. We consider the MIMO output error state space model identification, the so-called MOESP. Making a comparison between the matrix obtained by the QR factorization in the MOESP and the Schur complement matrix of data product moments shows that the estimate of the extended observability matrix can be obtained by using the SES procedure. Viewing that fact that the Schur complement yielded by the subspace extraction coincides with the error covariance in the least squares (LS), our interpretation will pave the way for the derivation of the recursive algorithm of the 4SID method.

AB - In this paper, we present a new interpretation of the subspace-based state space system identification (4SID) method by using a subspace extraction via Schur complement (SES). Several efficient implementations of subspace-based identification methods (e.g., N4SID, etc) have been thus far developed and proposed. We consider the MIMO output error state space model identification, the so-called MOESP. Making a comparison between the matrix obtained by the QR factorization in the MOESP and the Schur complement matrix of data product moments shows that the estimate of the extended observability matrix can be obtained by using the SES procedure. Viewing that fact that the Schur complement yielded by the subspace extraction coincides with the error covariance in the least squares (LS), our interpretation will pave the way for the derivation of the recursive algorithm of the 4SID method.

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