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Further Results on Model Structure Validation for Closed Loop System Identification

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), 2017. Published by Science Publishing Group

Keywords

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

References
[1] Urban Forssel, Lennart Ljung, “Closed loop identification revisted,” Automatica, vol. 35, no. 7, pp. 1215-1241, 1999.
[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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  • 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

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

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

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