RECURSIVE BIAS-COMPENSATING ALGORITHM FOR THE IDENTIFICATION OF DYNAMICAL BILINEAR SYSTEMS IN THE ERRORS-IN-VARIABLES FRAMEWORK

T. Larkowski, J. G. Linden, B. Vinsonneau, K. J. Burnham

Abstract

The paper investigates a recursive approach for the bias compensating least squares (BCLS) technique. The method presented is applied to the problem of on-line identification of single-input single-output bilinear models in the errors-in-variables framework. Within this framework the recursive bilinear BCLS algorithm is realized when a bilinear Frisch scheme (BFS) is iteratively applied for the estimation of the parameters of an exemplary bilinear system, giving rise to the exact recursive BFS (ERBFS) method. Moreover, a further extension of the ERBFS incorporating Tikhonov regularization with variable exponential weighting is considered and this is shown to be beneficial in the initial period of the identification procedure.

References

  1. Beghelli, S., Guidorzi, R. P., and Soverini, U. (1990). The Frisch scheme in dynamic system identification. Automatica, 26(1):171-176.
  2. Burnham, K. J. (1991). Self-tuning Control for Bilinear Systems. PhD thesis, Coventry Polytechnic.
  3. Diversi, R., Guidorzi, R., and Soverini, U. (2006). YuleWalker equations in the Frisch scheme solution of errors-in-variables identification problems. In Proc. of the 17th Int. Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan.
  4. Ekman, M. (2005). Modeling and Control of Bilinear Systems: Applications to the Activated Sludge Process. PhD thesis, Uppsala University.
  5. Hansen, P. C. (2001). Regularization tools: A matlab package for analysis and solution of discrete ill-posed problems. Technical report, Department of Mathematical Modelling, Technical University of Denmark.
  6. Ikonen, E. and Najim, K. (2002). Advanced Process Identification and Control. Marcel Dekker, Inc., USA.
  7. Kotta, U. and Nomm, S.and Zinober, A. (2003). On state space realizability of bilinear systems described by higher order difference equations. In Proc. of 42nd IEEE Conf. on Decision and Control, volume 6, pages 5685-5690.
  8. Larkowski, T., Linden, J. G., Vinsonneau, B., and Burnham, K. J. (2008). A novel errors-in-variables approach for bilinear models: the bilinear Frisch scheme. Internal report no. CTAC/TL-1/2008, Control Theory and Applications Centre, Coventry University, Coventry.
  9. Larkowski, T., Vinsonneau, B., and Burnham, K. J. (2007). Bilinear model identification in the errors-in-variables framework via the bias-compensating least squares. In IAR and ACD Int. Conf., Grenoble, France.
  10. Linden, G. J., Vinsonneau, B., and Burnham, K. J. (2007). Fast algorithms for recursive Frisch scheme system identification. In IAR and ACD Int. Conf., Grenoble, France.
  11. Liu, J. (1992). On stationarity and asymptotic inference of bilinear time series models. Statistica Sinica, 2:479- 494.
  12. Ljung, L. (1999). System Identification - Theory for the User. Prentice Hall PTR, New Jersey, USA, 2nd edition edition.
  13. Ljung, L. and S öderström, T. (1987). Theory and practice of recursive identification. MIT Press, Cambridge, UK.
  14. Martineau, S., Burnham, K. J., Haas, O. C. L., Andrews, G., and Heeley, A. (2004). Four-term bilinear pid controller applied to an industrial furnace. Control Engineering Practice, 12(4):457-464.
  15. Mohler, R. R. (1991). Nonlinear Systems: Applications to Bilinear Control, volume 2. Prentice Hall, Englewood Cliffs, NJ.
  16. Mohler, R. R. and Khapalov, A. Y. (2000). Bilinear control and application to flexible a.c. transmission systems. Journal of Optimization Theory and Applications, 105(3):621-637.
  17. Pearson, R. K. (1999). Discrete-Time Dynamic Models. Oxford University Press, New York, USA.
  18. Rao, T. S. and Gabr, M. M. (1984). An Introduction to Bispectral Analysis and Bilinear Time Series Models. Springer-Verlag, Berlin, Germany.
  19. S öderström, T. (2006). Statistical analysis of the Frisch scheme for identifying errors-in-variables systems. Technical report, Upsala Univercity, Department of Information Technology, Upsala, Sweden.
  20. S öderström, T. (2007). Errors-in-variables methods in system identification. In Automatica, volume 43, pages 939-958.
  21. S öderström, T., Soverini, U., and Mahata, K. (2002). Perspectives on errors-in-variables estimation for dynamic systems. In Signal Processing, volume 82(8), pages 1139-1154.
  22. S öderström, T. and Stoica, P. (1994). System Identification. Prentice Hall Int., New Jersey, USA.
  23. Young, P. (1984). Recursive Estimation and Time-Series Analysis. Springer-Verlag, Berlin, Germany.
  24. Yu, D. (1996). Fault diagnosis for industrial systems with emphasis on bilinear systems. PhD thesis, Coventry University.
  25. Zheng, W. X. (1998). Transfer function estimation from noisy input and output data. Int. Journal of Adaptive Control and Signal Processing, 12:365-380.
  26. Zheng, W. X. (2000). Parametric identification of linear noisy input-output systems. Cybernetics and Systems, 31(7):803-816.
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Paper Citation


in Harvard Style

Larkowski T., G. Linden J., Vinsonneau B. and J. Burnham K. (2008). RECURSIVE BIAS-COMPENSATING ALGORITHM FOR THE IDENTIFICATION OF DYNAMICAL BILINEAR SYSTEMS IN THE ERRORS-IN-VARIABLES FRAMEWORK . In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-989-8111-32-6, pages 38-45. DOI: 10.5220/0001496000380045


in Bibtex Style

@conference{icinco08,
author={T. Larkowski and J. G. Linden and B. Vinsonneau and K. J. Burnham},
title={RECURSIVE BIAS-COMPENSATING ALGORITHM FOR THE IDENTIFICATION OF DYNAMICAL BILINEAR SYSTEMS IN THE ERRORS-IN-VARIABLES FRAMEWORK},
booktitle={Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2008},
pages={38-45},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001496000380045},
isbn={978-989-8111-32-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - RECURSIVE BIAS-COMPENSATING ALGORITHM FOR THE IDENTIFICATION OF DYNAMICAL BILINEAR SYSTEMS IN THE ERRORS-IN-VARIABLES FRAMEWORK
SN - 978-989-8111-32-6
AU - Larkowski T.
AU - G. Linden J.
AU - Vinsonneau B.
AU - J. Burnham K.
PY - 2008
SP - 38
EP - 45
DO - 10.5220/0001496000380045