Skip to main content
SpringerLink
Log in

Methods for Finding a Regularized Solution When Identifying Linear Multivariable Multiconnected Discrete Systems

  • SYSTEMS ANALYSIS
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

This article considers the problem of structural and parametric identification of a complex multi-input multi-output (MIMO) discrete system in a class of state-space models. It is assumed that only the input and output coordinates of the system on some time interval and the range of measurement errors are known. The subspace method (4SID) underlies this approach, which presumes that the dimension of the system (state vector) is known, which is not always fulfilled in practice. Moreover, the dependence on the noise level makes it impossible to correctly identify a high-dimensional system. Therefore, it is proposed to consider dimension as a regularizing parameter. Three methods are developed for choosing an approximate model dimension depending on the duration of the observation interval and the possibility of designing an active experiment. The proposed methods are approved by an example of the problem of identifying a cognitive map of a commercial bank in an impulse process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Ninness and G. C. Goodwin, “Estimation of model quality,” Automatica, Vol. 31, No. 12, 1771–1797 (1995).

    Article  MathSciNet  Google Scholar 

  2. L. Giarre, B. Z. Kacewicz, and M. Milanese, “Model quality evaluation in set membership identification,” Automatica, Vol. 33, No. 6, 1133–1139 (1997).

    Article  MathSciNet  Google Scholar 

  3. T. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, N.J. (1980).

  4. B. Ho and R. E. Kalman, “Effective construction of linear state-variable models from input/output functions,” Regelungstechnik, Vol. 14, 545–548 (1966).

  5. M. Verhaegen and P. Dewilde, “Subspace model identification. Part 1: The output-error state space model identification class of algorithms,” International Journal of Control, Vol. 56, No. 5, 1187–1210 (1992).

  6. P. Van Overschee and B. De Moor, “N4SID: Subspace algorithms for identification of combined deterministic-stochastic systems,” Automatica, Vol. 30, No. 1, 75–93 (1994).

  7. M. Verhaegen, “Identification of the deterministic part of MIMO state space models given in innovations form from input-output data,” Automatica, Vol. 30, No. 1, 61–74 (1994).

  8. P. Van Overschee and B. De Moor, Subspace Identification for Linear Systems, Kluwer, Boston–London–Dordrecht (1996).

  9. V. F. Gubarev, “Rational approximation of distributed parameter systems,” Cybernetics and Systems Analysis, Vol. 44, No. 2, 234–246 (2008).

    Article  MathSciNet  Google Scholar 

  10. A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving Incorrect Tasks [in Russian], Nauka, Moscow (1986).

  11. M. Viberg, “Subspace-based method for the identification of linear time-invariant systems,” Automatica, Vol. 31, No. 12, 1835–1851 (1996).

  12. L. Ljung, System Identification Toolbox User’s Guide, Mathworks, Natick MA (2014).

  13. G. V. Gorelova, E. N. Zakharova, and S. A. Radchenko, Study of Semi-Structured Problems of Socio-Economic Systems. The Cognitive Approach [in Russian], Publishing House of RSU, Rostov-on-Don (2006).

  14. F. S. Roberts, Discrete Mathematical Models, with Applications to Social, Biological and Environmental Problems [Russian translation], Nauka, Moscow (1986).

  15. V. F. Gubarev, V. D. Romanenko, and Yu. L. Milyavsky, “Identification in cognitive maps in the impulse processes mode with full information,” International Scientific Technical Journal “Problems of Control and Informatics,” No. 4, 30–43 (2018).

  16. Yu. L. Miliavskyi, “Identification in cognitive maps in impulse process mode with incomplete measurement of nodes coordinates,” Cybernetics and Computer Engineering, No. 1 (195), 49–63 (2019).

Download references

Author information

Authors and Affiliations

  1. Space Research Institute, National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kyiv, Ukraine

    V. F. Gubarev

  2. Institute for Applied Systems Analysis at the NTUU “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    V. D. Romanenko & Yu. L. Miliavskyi

Authors
  1. V. F. Gubarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. D. Romanenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. L. Miliavskyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. F. Gubarev.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2019, pp. 3–16.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gubarev, V.F., Romanenko, V.D. & Miliavskyi, Y.L. Methods for Finding a Regularized Solution When Identifying Linear Multivariable Multiconnected Discrete Systems. Cybern Syst Anal 55, 881–893 (2019). https://doi.org/10.1007/s10559-019-00198-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-019-00198-5

Keywords

Search

Navigation