Application of structured total least squares for system identification and model reduction
Application of structured total least squares for system identification and model reduction
The following identification problem is considered: minimize the l2 norm of the difference between a given time series and an approximating one under the constraint that the approximating time series is a trajectory of a linear time invariant system of a fixed complexity. The complexity is measured by the input dimension and the maximum lag. The problem is known as the global total least squares and alternatively can be viewed as maximum likelihood identification in the errors-in-variables setup. Multiple time series and latent variables can be considered in the same setting. Special cases of the problem are autonomous system identification, noisy realization, and finite time optimal l2 model reduction. The identification problem is related to the structured total least squares problem. The paper presents an efficient software package that implements the theory in practice. The proposed method and software are tested on data sets from the database for the identification of systems DAISY.
Errors-in-variables, system identification, model reduction, structured total least squares, numerical software, DAISY, MPUM.
1490-1500
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Willems, J. C.
b65cabbf-8134-4199-a8fa-4aaba1950705
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
De Moor, B.
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Pintelon, R.
4c9f21b0-f905-49fb-8163-57e410bbc974
Ljung, L.
29a4371e-8060-4aaf-9b10-333bc62a0b4b
2005
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Willems, J. C.
b65cabbf-8134-4199-a8fa-4aaba1950705
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
De Moor, B.
f25df85a-5050-448e-bd50-a278455f5b47
Pintelon, R.
4c9f21b0-f905-49fb-8163-57e410bbc974
Ljung, L.
29a4371e-8060-4aaf-9b10-333bc62a0b4b
Markovsky, I., Willems, J. C., Van Huffel, S., De Moor, B. and Pintelon, R.
,
Ljung, L.
(ed.)
(2005)
Application of structured total least squares for system identification and model reduction.
IEEE Transactions on Automatic Control, 50 (10), .
Abstract
The following identification problem is considered: minimize the l2 norm of the difference between a given time series and an approximating one under the constraint that the approximating time series is a trajectory of a linear time invariant system of a fixed complexity. The complexity is measured by the input dimension and the maximum lag. The problem is known as the global total least squares and alternatively can be viewed as maximum likelihood identification in the errors-in-variables setup. Multiple time series and latent variables can be considered in the same setting. Special cases of the problem are autonomous system identification, noisy realization, and finite time optimal l2 model reduction. The identification problem is related to the structured total least squares problem. The paper presents an efficient software package that implements the theory in practice. The proposed method and software are tested on data sets from the database for the identification of systems DAISY.
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Published date: 2005
Keywords:
Errors-in-variables, system identification, model reduction, structured total least squares, numerical software, DAISY, MPUM.
Organisations:
Southampton Wireless Group
Identifiers
Local EPrints ID: 263300
URI: http://eprints.soton.ac.uk/id/eprint/263300
ISSN: 0018-9286
PURE UUID: 902d5088-af8d-4425-b65f-9c7fb9f9d01b
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Date deposited: 06 Jan 2007
Last modified: 14 Mar 2024 07:29
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Contributors
Author:
I. Markovsky
Author:
J. C. Willems
Author:
S. Van Huffel
Author:
B. De Moor
Author:
R. Pintelon
Editor:
L. Ljung
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