Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 328186, 18 pages
http://dx.doi.org/10.1155/2012/328186
Research Article

Iterative System Identification and Controller Design with an LMI-Based Framework: Windsurfer-Like Approach

Department of Mechanical and Production Engineering, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan

Received 1 March 2012; Revised 21 June 2012; Accepted 24 June 2012

Academic Editor: Xianxia Zhang

Copyright © 2012 Kazuhiko Hiramoto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. E. Skelton, “Model error concepts in control design,” International Journal of Control, vol. 49, no. 5, pp. 1725–1753, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. P. M. J. van den Hof and R. J. P. Schrama, “Identification and control—closed-loop issues,” Automatica, vol. 31, no. 12, pp. 1751–1770, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. U. Forssell and L. Ljung, “Closed-loop identification revisited,” Automatica, vol. 35, no. 7, pp. 1215–1241, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. Gevers, X. Bombois, B. Codrons, G. Scorletti, and B. D. O. Anderson, “Model validation for control and controller validation in a prediction error identification framework—part I: theory,” Automatica, vol. 39, no. 3, pp. 403–415, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. M. Okada, H. Fukushima, and T. Sugie, “Joint design of model-subspace based identification and control,” in Proceedings of the 11th IFAC Symposium on System Identification, vol. 3, pp. 1155–1160, 1997.
  6. H. Ichihara, Y. Matsumoto, N. Abe, and H. Kanoh, “Application of an iterative identification and control design to a vibration system,” JSME International Journal, vol. 43, no. 1, pp. 18–24, 2000. View at Publisher · View at Google Scholar
  7. W. S. Lee, B. D. O. Anderson, I. M. Y. Mareels, and R. L. Kosut, “On some key issues in the windsurfer approach to adaptive robust control,” Automatica, vol. 31, no. 11, pp. 1619–1636, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. Dehghani, A. Lanzon, and B. D. O. Anderson, “An algorithm for the windsurfer approach to adaptive robust control,” International Journal of Adaptive Control and Signal Processing, vol. 18, no. 8, pp. 607–628, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Lecchini, A. Lanzon, and B. D. O. Anderson, “A model reference approach to safe controller changes in iterative identification and control,” Automatica, vol. 42, no. 2, pp. 193–203, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Garatti, M. C. Campi, and S. Bittanti, “Iterative robust control: speeding up improvement through iterations,” Systems & Control Letters, vol. 59, no. 2, pp. 139–146, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Z. Zang, R. R. Bitmead, and M. Gevers, “Iterative weighted least-squares identification and weighted LQG control design,” Automatica, vol. 31, no. 11, pp. 1577–1594, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. F. R. Hansen, G. Franklin, and R. Kosut, “Closed-loop identification via the fractional representation: experiment design,” in Proceedings of the American Control Conference, pp. 1422–1427, Pittsburgh, Pa, USA, June 1989. View at Scopus
  13. Y. J. Liu, Y. S. Xiao, and X. L. Zhao, “Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model,” Applied Mathematics and Computation, vol. 215, no. 4, pp. 1477–1483, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. H. Li and F. Ding, “Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique,” Computers & Mathematics with Applications, vol. 62, no. 11, pp. 4170–4177, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. J. Ding, F. Ding, X. P. Liu, and G. Liu, “Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data,” Institute of Electrical and Electronics Engineers, vol. 56, no. 11, pp. 2677–2683, 2011. View at Publisher · View at Google Scholar
  16. D. Q. Wang, “Least squares-based recursive and iterative estimation for output error moving average systems using data filtering,” IET Control Theory & Applications, vol. 5, no. 14, pp. 1648–1657, 2011. View at Publisher · View at Google Scholar
  17. Y. J. Liu, J. Sheng, and R. F. Ding, “Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems,” Computers & Mathematics with Applications, vol. 59, no. 8, pp. 2615–2627, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. F. Ding, X. P. Liu, and G. Liu, “Identification methods for Hammerstein nonlinear systems,” Digital Signal Processing, vol. 21, no. 2, pp. 215–238, 2011. View at Publisher · View at Google Scholar
  19. F. Ding, G. Liu, and X. P. Liu, “Partially coupled stochastic gradient identification methods for non-uniformly sampled systems,” Institute of Electrical and Electronics Engineers, vol. 55, no. 8, pp. 1976–1981, 2010. View at Publisher · View at Google Scholar
  20. G. Vinnicombe, Uncertainty and Feedback— Loop-Shaping and the ν-Gap Metric, Imperial College Press, Amsterdam, The Netherlands, 2001.
  21. M. C. de Oliveira, J. C. Geromel, and J. Bernussou, “Extended H2 and H norm characterizations and controller parametrizations for discrete-time systems,” International Journal of Control, vol. 75, no. 9, pp. 666–679, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. P. M. J. van den Hof and R. J. P. Schrama, “An indirect method for transfer function estimation from closed loop data,” Automatica, vol. 29, no. 6, pp. 1523–1527, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. H. Hjalmarsson, “Iterative feedback tuning—an overview,” International Journal of Adaptive Control and Signal Processing, vol. 16, no. 5, pp. 373–395, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. M. C. Campi, A. Lecchini, and S. M. Savaresi, “Virtual reference feedback tuning: a direct method for the design of feedback controllers,” Automatica, vol. 38, no. 8, pp. 1337–1346, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH