Skip to main content
SpringerLink
Log in

Subspace-based Continuous-time Identification

  • Chapter
Identification of Continuous-time Models from Sampled Data

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

The last few years have witnessed a strong interest in system identification using realisation-based algorithms. The use of Markov parameters as suggested by Ho and Kalman [18] Akaike [1], and Kung [28], of a system can be effectively applied to the problem of state-space identification; see Verhaegen et al. [43, 44], van Overschee and de Moor [41], Juang and Pappa [26], Moonen et al. [36], Bayard [3, 4, 33, 34]. Suitable background for the discrete-time theory supporting stochastic subspace model identification is to be found in [1,14,41]. As for model structures and realisation theory, see the important contributions [12, 31]. As these subspace-model identification algorithms deal with the case of fitting a discrete-time model, it remains as an open problem how to extend these methods for continuous-time (CT) systems. A great deal of modelling in natural sciences and technology is made by means of continuous-time models and such models require suitable methods of system identification [19]. To this end, a theoretical framework of continuous-time identification and statistical model validation is needed. In particular, as experimental data are usually provided as time series, it is relevant to provide continuous-time theory and algorithms that permit application to discrete-time data.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Akaike. Markovian representation of stochastic processes by canonical variables. SIAM Journal of Control, 13:162–173, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  2. B.D.O. Anderson and P.J. Moylan. Spectral factorization of a finite-dimensional nonstationary matrix covariance. IEEE Transactions on Automatic Control, AC-19(6):680–692, 1974.

    Article  MathSciNet  Google Scholar 

  3. D.S. Bayard. An algorithm for state-space frequency domain identification without windowing distortions. IEEE Transactions on Automatic Control, 39(9):1880–1885, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Bigi, T. Söderström, and B. Carlsson. An IV-scheme for estimating continuous-time stochastic models from discrete-time data. 10th IFAC Symposium on System Identification (SYSID’94), volume 3, pages 645–650, Copenhagen, Denmark, 1994.

    Google Scholar 

  5. C.T. Chou, M. Verhaegen, and R. Johansson. Continuous-time identification of SISO systems using Laguerre functions. IEEE Transactions on Signal Processing, 47:349–362, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Deistler, K. Peternell, and W. Scherrer. Consistency and relative efficiency of subspace methods. Automatica, 31(12):1865–1875, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  7. U.B. Desai and D. Pal. A realisation approach to stochastic model reduction and balanced stochastic realisations. IEEE Conference on Decision and Control (CDC’1982), pages 1105–1112, Orlando, FL, USA, 1982.

    Google Scholar 

  8. B.W. Dickinson, T. Kailath, and M. Morf. Canonical matrix fraction and state-space description for deterministic and stochastic linear systems. IEEE Transactions on Automatic Control, AC-19:656–667, 1974.

    Article  MathSciNet  Google Scholar 

  9. P. Faurre. Stochastic realisation algorithms. In R.K. Mehra and D. Lainiotis (eds), System identification: Advances and Case Studies. Academic Press, New York, USA, 1976.

    Google Scholar 

  10. H. Garnier, M. Gilson, and E. Huselstein. Developments for the Matlab CONTSID Toolbox. 13th IFAC Symposium on System Identification (SYSID’2003), Rotterdam, The Netherlands, 2003.

    Google Scholar 

  11. H. Garnier, M. Mensler, and A. Richard. Continuous-time model identification from sampled data: Implementation issues and performance evaluation. International Journal of Control, 76(13):1337–1357, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. Guidorzi. Canonical structures in the identification of multivariable systems. Automatica, 11:361–374, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Hagander and A. Hansson. How to solve singular discrete-time Riccati equations. 13th IFAC World Congress, pages 313–318, San Francisco, CA, USA, July 1996.

    Google Scholar 

  14. E.J. Hannan and M. Deistler. The Statistical Theory of Linear Systems. Wiley, New York, 1988.

    MATH  Google Scholar 

  15. B.R.J. Haverkamp, M. Verhaegen, C.T. Chou, and R. Johansson. Tuning of the continuous-time Kalman filter from sampled data. IEEE American Control Conference (ACC’99), pages 3895–3899, San Diego, CA, USA, June 1999.

    Google Scholar 

  16. B.R.J. Haverkamp, C.T. Chou, M. Verhaegen, and R. Johansson. Identification of continuous-time MIMO state space models from sampled data, in the presence of process and measurement noise. 36th IEEE Conference on Decision and Control (CDC’96), pages 1539–1544, Kobe, Japan, December 1996.

    Google Scholar 

  17. L.R.J. Haverkamp. State Space Identification-Theory and Practice. PhD thesis, T. U. Delft, Delft, The Netherlands, 2001.

    Google Scholar 

  18. B.L. Ho and R.E. Kalman. Effective construction of linear state-variable models from input/output functions. Regelungstechnik, 14:545–548, 1966.

    MATH  Google Scholar 

  19. R. Johansson. System Modeling and Identification. Prentice Hall, Englewood Cliffs, NJ, USA, 1993.

    Google Scholar 

  20. R. Johansson. Identification of continuous-time models. IEEE Transactions on Signal Processing, 42(4):887–897, 1994.

    Article  Google Scholar 

  21. R. Johansson and G. Lindstedt. An algorithm for continuous-time state space identification. 34th IEEE Conference on Decision and Control (CDC’95), pages 721–722, New Orleans, LA, USA, 1995.

    Google Scholar 

  22. R. Johansson, M. Verhaegen, and C.T. Chou. Stochastic theory of continuous-time state-space identification. 37th IEEE Conference on Decision and Control (CDC’97), pages 1866–1871, San Diego, CA, USA, 1997.

    Google Scholar 

  23. R. Johansson, M. Verhaegen, and C.T. Chou. Stochastic theory of continuous-time state-space identification. IEEE Transactions on Signal Processing, 47:41–51, January 1999.

    Article  MATH  MathSciNet  Google Scholar 

  24. R. Johansson, M. Verhaegen, C.T. Chou, and A. Robertsson. Residual models and stochastic realisation in state-space identification. International Journal of Control, 74(10):988–995, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  25. J.N. Juang. Applied System Identification. Prentice Hall, Englewood Cliffs, NJ, USA, 1994.

    MATH  Google Scholar 

  26. J.N. Juang and R.S. Pappa. An eigensystem realisation algorithm for modal parameter identification and model reduction. Journal of Guidance, Control and Dynamics, 8:620–627, 1985.

    Article  MATH  Google Scholar 

  27. T. Katayama. Subspace Methods for System Identification. Springer-Verlag, London, UK, 2005.

    MATH  Google Scholar 

  28. S.Y. Kung. A new identification and model reduction algorithm via singular value decomposition. 12th Asilomar Conference on Circuits, Systems and Computers, pages 705–714, Pacific Grove, CA, USA, 1978.

    Google Scholar 

  29. W. Larimore. Canonical variate analysis in identification, filtering and adaptive control. 29th IEEE Conference Decision and Control (CDC’90), pages 596–604, Hawaii, USA, 1990.

    Google Scholar 

  30. W. Li, H. Raghavan, and S. Shah. Subspace identification of continuous-time models for process fault detection and isolation. Journal of Process Control, 13(5):407–421, 2003.

    Article  Google Scholar 

  31. A. Lindquist and G. Picci. Realisation theory for multivariate stationary Gaussian processes. SIAM Journal of Control and Optimisation, 23(6):809–857, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  32. K. Mahata and H. Garnier. Identification of continuous-time errors-in-variables models. Automatica, 42(9):1470–1490, 2006.

    Article  MathSciNet  Google Scholar 

  33. T. McKelvey and H. Akçay. An efficient frequency domain state-space identification algorithm. 33rd IEEE Conference on Decision and Control (CDC’1994), pages 3359–3364, 1994.

    Google Scholar 

  34. T. McKelvey and H. Akçay. An efficient frequency domain state-space identification algorithm: Robustness and stochastic analysis. 33rd IEEE Conference on Decision and Control (CDC’1994), pages 3348–3353, 1994.

    Google Scholar 

  35. T. McKelvey, H. Akçay, and L. Ljung. Subspace-based multivariable system identification from frequence response data. IEEE Transactions on Automatic Control, 41:960–979, 1996.

    Article  MATH  Google Scholar 

  36. M. Moonen, B. de Moor, L. Vandenberghe, and J. Vandewalle. On-and off-line identification of linear state-space models. International Journal of Control, 49:219–232, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  37. A. Ohsumi, K. Kameyama, and K.-I. Yamaguchi. Subspace identification for continuous-time stochastic systems via distribution-based approach. Automatica, 38(1):63–79, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  38. P. Van Overschee and B. De Moor. N4SID: subspace algorithm for the identification of combined deterministic-stochastic systems. Automatica, 30:75–93, 1994.

    Article  MATH  Google Scholar 

  39. K. Peternell, W. Scherrer, and M. Deistler. Statistical analysis of novel subspace identification methods. Signal Processing, 52(2):161–177, 1996.

    Article  MATH  Google Scholar 

  40. T. Ribarits, M. Deistler, and B. Hanzon. On new parametrization methods for the estimation of linear state-space models. International Journal of Adaptive Control and Signal Processing, 18(9–10):717–743, 2004.

    Article  MATH  Google Scholar 

  41. P. van Overschee and B. de Moor. Subspace Identification for Linear Systems—Theory, Implementation, Applications. Kluwer Academic Publishers, Boston-London-Dordrecht, 1996.

    MATH  Google Scholar 

  42. M. Verhaegen. Identification of the deterministic part of MIMO state space models given in innovation form from input-output data. Special Issue on Statistical Signal Processing and Control, Automatica, 30(1):61–74, 1994.

    MATH  MathSciNet  Google Scholar 

  43. M. Verhaegen and P. Dewilde. Subspace model identification—Analysis of the elementary output-error state-space model identification algorithm. International Journal of Control, 56:1211–1241, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  44. M. Verhaegen and P. Dewilde. Subspace model identification-The output-error state-space model identification class of algorithms. International Journal of Control, 56:1187–1210, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  45. L. Wang. Continuous time model predictive control design using orthonormal functions. International Journal of Control, 74:1588–1600, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  46. L. Wang. Discrete model predictive controller design using Laguerre function. Journal Process of Control, 14:131–142, 2004.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lund University, Sweden

    Rolf Johansson

Authors
  1. Rolf Johansson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculté des Sciences et Techniques, Centre de Recherche en Automatique de Nancy (CRAN), Nancy-Université CNRS, 54506, Vandoeuvre-les-Nancy, France

    Hugues Garnier PhD

  2. School of Electrical and Computing Engineering, RMIT University, Swanston Street, Melbourne, 3000, Victoria, Australia

    Liuping Wang PhD

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag London Limited

About this chapter

Cite this chapter

Johansson, R. (2008). Subspace-based Continuous-time Identification. In: Garnier, H., Wang, L. (eds) Identification of Continuous-time Models from Sampled Data. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-84800-161-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-84800-161-9_10

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84800-160-2

  • Online ISBN: 978-1-84800-161-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation