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Residual Models and Stochastic Realization in State-Space Identification

Johansson, Rolf LU ; Verhaegen, Michel; Chou, C.T. and Robertsson, Anders LU (2001) In International Journal of Control 74(10). p.988-995
Abstract
This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system... (More)
This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal of Control
volume
74
issue
10
pages
988 - 995
publisher
Taylor & Francis
external identifiers
  • scopus:0035838740
ISSN
0020-7179
DOI
10.1080/00207170110049855
language
English
LU publication?
yes
id
f69e8c1d-b4d3-48a0-9d62-d85bf5daac34 (old id 162839)
date added to LUP
2007-07-05 11:11:28
date last changed
2018-01-07 05:28:16
@article{f69e8c1d-b4d3-48a0-9d62-d85bf5daac34,
  abstract     = {This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.},
  author       = {Johansson, Rolf and Verhaegen, Michel and Chou, C.T. and Robertsson, Anders},
  issn         = {0020-7179},
  language     = {eng},
  number       = {10},
  pages        = {988--995},
  publisher    = {Taylor & Francis},
  series       = {International Journal of Control},
  title        = {Residual Models and Stochastic Realization in State-Space Identification},
  url          = {http://dx.doi.org/10.1080/00207170110049855},
  volume       = {74},
  year         = {2001},
}