Further Results on Model Structure Validation for Closed Loop System Identification

Wang Jian-hong; Wang Yan-xiang

doi:doi:10.11648/j.awcn.20170305.12

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Further Results on Model Structure Validation for Closed Loop System Identification

Wang Jian-hong, Wang Yan-xiang

Published in Advances in Wireless Communications and Networks (Volume 3, Issue 5)

Received: 18 May 2017 Accepted: 28 June 2017 Published: 24 August 2017

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Abstract

In this paper, further results on the problem of the model structure validation for closed loop system identification are proposed. One probabilistic model uncertainty is derived from some statistical properties of the parameter estimation. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix. Further a new technique for estimating bias and variance contributions to the model error is suggested. One bound described as an inequality corresponds to a condition on the model error. Due to this proposed bound, model structure validation process can be transformed to verify whether the model error obeys this inequality. Finally the simulation example results confirm the identification theoretical results.

Published in	Advances in Wireless Communications and Networks (Volume 3, Issue 5)
DOI	10.11648/j.awcn.20170305.12
Page(s)	57-66
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Closed Loop Identification, Model Uncertainty, Model Structure Validity, One Bound

References

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[2]	Ljung, L, “System identification: Theory for the user,” Prentice Hall, 1999.
[3]	Pintelon R, Schoukens J, “System identification: a frequency domain approach,” New York: IEEE Press, 2001.
[4]	Juan C, Augero, “A virtual closed loop method for closed loop identification,” Automatica, vol 47, no. 8, pp. 1626-1637, 2011.
[5]	U, Forssell, L Ljung, “Some results on optimal experiment design,” Automatica, vol 36, no. 5, pp. 749-756, 2000.
[6]	M, Leskers, “Closed loop identification of multivariable process with part of the inputs controlled,” International Journal of Control, vol 80, no. 10, pp. 1552-1561, 2007.
[7]	Hakan Hjalmarssion, “From experiment design to closed loop control,” Automatica, vol 41, no. 3, pp. 393-438, 2005.
[8]	Hakan Hjalmarssion, “Closed loop experiment design for linear time invariant dynamical systems via LMI,” Automatica, vol 44, no. 3, pp. 623-636, 2008.
[9]	X, Bombois, “Least costly identification experiment for control,” Automatica, vol 42, no. 10, pp. 1651-1662, 2006.
[10]	Roland Hildebrand, “Identification for control: optimal input design with respect to a worst case gap cost function,” SIAM Journal of Control Optimization, vol 41, no. 5, pp. 1586-1608, 2003.
[11]	M, Gevers, “Identification of multi input systems: variance analysis and input design issues,” Automatica, vol 42, no. 410, pp. 559-572, 2006.
[12]	M, Gevers, “Identification and information matrix: how to get just sufficiently rich,” IEEE Transactions on Automatic control, vol 54, no. 12, pp. 2828-2840, 2009.
[13]	Graham C Goodin, “Bias issues in closed loop identification with application to adaptive control,” Communications in Information and Systems, vol 2, no. 4, pp. 349-370, 2002.
[14]	James S Welsh, “Finite sample properties of indirect nonparametric closed loop identification,” IEEE Transactions on Automatic control, vol 47, no. 8, pp. 1277-1291, 2002.
[15]	Sippe G Douma, “Validity of the standard cross correlation test for model structure validation,” Automatica, vol 44, no. 4, pp. 1285-1294, 2008.
[16]	Wang Jian-hong, Wang Yan-xiang. “Model structure validation for closed loop system identification,” International Journal of Modelling, Identification and Control, vol 27, no. 4, pp. 323-331, 2017.

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Wang Jian-hong, Wang Yan-xiang. (2017). Further Results on Model Structure Validation for Closed Loop System Identification. Advances in Wireless Communications and Networks, 3(5), 57-66. https://doi.org/10.11648/j.awcn.20170305.12

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Wang Jian-hong; Wang Yan-xiang. Further Results on Model Structure Validation for Closed Loop System Identification. Adv. Wirel. Commun. Netw. 2017, 3(5), 57-66. doi: 10.11648/j.awcn.20170305.12

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AMA Style

Wang Jian-hong, Wang Yan-xiang. Further Results on Model Structure Validation for Closed Loop System Identification. Adv Wirel Commun Netw. 2017;3(5):57-66. doi: 10.11648/j.awcn.20170305.12

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@article{10.11648/j.awcn.20170305.12,
  author = {Wang Jian-hong and Wang Yan-xiang},
  title = {Further Results on Model Structure Validation for Closed Loop System Identification},
  journal = {Advances in Wireless Communications and Networks},
  volume = {3},
  number = {5},
  pages = {57-66},
  doi = {10.11648/j.awcn.20170305.12},
  url = {https://doi.org/10.11648/j.awcn.20170305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.awcn.20170305.12},
  abstract = {In this paper, further results on the problem of the model structure validation for closed loop system identification are proposed. One probabilistic model uncertainty is derived from some statistical properties of the parameter estimation. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix. Further a new technique for estimating bias and variance contributions to the model error is suggested. One bound described as an inequality corresponds to a condition on the model error. Due to this proposed bound, model structure validation process can be transformed to verify whether the model error obeys this inequality. Finally the simulation example results confirm the identification theoretical results.},
 year = {2017}
}

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TY  - JOUR
T1  - Further Results on Model Structure Validation for Closed Loop System Identification
AU  - Wang Jian-hong
AU  - Wang Yan-xiang
Y1  - 2017/08/24
PY  - 2017
N1  - https://doi.org/10.11648/j.awcn.20170305.12
DO  - 10.11648/j.awcn.20170305.12
T2  - Advances in Wireless Communications and Networks
JF  - Advances in Wireless Communications and Networks
JO  - Advances in Wireless Communications and Networks
SP  - 57
EP  - 66
PB  - Science Publishing Group
SN  - 2575-596X
UR  - https://doi.org/10.11648/j.awcn.20170305.12
AB  - In this paper, further results on the problem of the model structure validation for closed loop system identification are proposed. One probabilistic model uncertainty is derived from some statistical properties of the parameter estimation. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix. Further a new technique for estimating bias and variance contributions to the model error is suggested. One bound described as an inequality corresponds to a condition on the model error. Due to this proposed bound, model structure validation process can be transformed to verify whether the model error obeys this inequality. Finally the simulation example results confirm the identification theoretical results.
VL  - 3
IS  - 5
ER  -

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Author Information

Wang Jian-hong

School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, China
Wang Yan-xiang

School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, China

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APA Style

Wang Jian-hong, Wang Yan-xiang. (2017). Further Results on Model Structure Validation for Closed Loop System Identification. Advances in Wireless Communications and Networks, 3(5), 57-66. https://doi.org/10.11648/j.awcn.20170305.12

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ACS Style

Wang Jian-hong; Wang Yan-xiang. Further Results on Model Structure Validation for Closed Loop System Identification. Adv. Wirel. Commun. Netw. 2017, 3(5), 57-66. doi: 10.11648/j.awcn.20170305.12

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AMA Style

Wang Jian-hong, Wang Yan-xiang. Further Results on Model Structure Validation for Closed Loop System Identification. Adv Wirel Commun Netw. 2017;3(5):57-66. doi: 10.11648/j.awcn.20170305.12

Copy | Download

@article{10.11648/j.awcn.20170305.12,
  author = {Wang Jian-hong and Wang Yan-xiang},
  title = {Further Results on Model Structure Validation for Closed Loop System Identification},
  journal = {Advances in Wireless Communications and Networks},
  volume = {3},
  number = {5},
  pages = {57-66},
  doi = {10.11648/j.awcn.20170305.12},
  url = {https://doi.org/10.11648/j.awcn.20170305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.awcn.20170305.12},
  abstract = {In this paper, further results on the problem of the model structure validation for closed loop system identification are proposed. One probabilistic model uncertainty is derived from some statistical properties of the parameter estimation. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix. Further a new technique for estimating bias and variance contributions to the model error is suggested. One bound described as an inequality corresponds to a condition on the model error. Due to this proposed bound, model structure validation process can be transformed to verify whether the model error obeys this inequality. Finally the simulation example results confirm the identification theoretical results.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Further Results on Model Structure Validation for Closed Loop System Identification
AU  - Wang Jian-hong
AU  - Wang Yan-xiang
Y1  - 2017/08/24
PY  - 2017
N1  - https://doi.org/10.11648/j.awcn.20170305.12
DO  - 10.11648/j.awcn.20170305.12
T2  - Advances in Wireless Communications and Networks
JF  - Advances in Wireless Communications and Networks
JO  - Advances in Wireless Communications and Networks
SP  - 57
EP  - 66
PB  - Science Publishing Group
SN  - 2575-596X
UR  - https://doi.org/10.11648/j.awcn.20170305.12
AB  - In this paper, further results on the problem of the model structure validation for closed loop system identification are proposed. One probabilistic model uncertainty is derived from some statistical properties of the parameter estimation. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix. Further a new technique for estimating bias and variance contributions to the model error is suggested. One bound described as an inequality corresponds to a condition on the model error. Due to this proposed bound, model structure validation process can be transformed to verify whether the model error obeys this inequality. Finally the simulation example results confirm the identification theoretical results.
VL  - 3
IS  - 5
ER  -

Copy | Download