Identification of stable models in subspace identification by using regularization

In subspace identification methods, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. For a finite number of data points, the estimated system matrix is not guaranteed to be stable, even when the true lin...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2001-09, Vol.46 (9), p.1416-1420
Main Authors: Van Gestel, T., Suykens, J.A.K., Van Dooren, P., De Moor, B.
Format: Article
Language:English
Subjects:
Covariance matrix
Data points
Dynamical systems
Eigenvalues
Eigenvalues and eigenfunctions
Gaussian noise
Government
Least squares approximation
Linear systems
Mathematical analysis
Matrices
Noise measurement
Regularization
Stability
State estimation
Stochastic resonance
Subspaces
Weighting
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Summary:In subspace identification methods, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. For a finite number of data points, the estimated system matrix is not guaranteed to be stable, even when the true linear system is known to be stable. In this paper, stability is imposed by using regularization. The regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive (semi) definite weighting matrix. The amount of regularization can be determined from a generalized eigenvalue problem. The data augmentation method of Chui and Maciejowski (1996) is obtained by using specific choices for the weighting matrix in the regularization term.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.948469