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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 684074, 14 pages
http://dx.doi.org/10.1155/2012/684074
Research Article

Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

1Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi 214122, China
2School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China

Received 18 March 2012; Accepted 26 April 2012

Academic Editor: Morteza Rafei

Copyright © 2012 Weili Xiong et al. 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. M. R. Zakerzadeh, M. Firouzi, H. Sayyaadi, and S. B. Shouraki, “Hysteresis nonlinearity identification using new Preisach model-based artificial neural network approach,” Journal of Applied Mathematics, Article ID 458768, 22 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. X.-X. Li, H. Z. Guo, S. M. Wan, and F. Yang, “Inverse source identification by the modified regularization method on poisson equation,” Journal of Applied Mathematics, vol. 2012, Article ID 971952, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. Shi and H. Fang, “Kalman filter-based identification for systems with randomly missing measurements in a network environment,” International Journal of Control, vol. 83, no. 3, pp. 538–551, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. Y. Liu, J. Sheng, and R. 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
  5. F. Ding, G. Liu, and X. P. Liu, “Parameter estimation with scarce measurements,” Automatica, vol. 47, no. 8, pp. 1646–1655, 2011. View at Google Scholar · View at Scopus
  6. J. Ding, F. Ding, X. P. Liu, and G. Liu, “Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data,” IEEE Transactions on Automatic Control, vol. 56, no. 11, pp. 2677–2683, 2011. View at Publisher · View at Google Scholar
  7. Y. Liu, Y. Xiao, and X. 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
  8. J. Ding and F. Ding, “The residual based extended least squares identification method for dual-rate systems,” Computers & Mathematics with Applications, vol. 56, no. 6, pp. 1479–1487, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. L. Han and F. Ding, “Identification for multirate multi-input systems using the multi-innovation identification theory,” Computers & Mathematics with Applications, vol. 57, no. 9, pp. 1438–1449, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. F. Ding, Y. Shi, and T. Chen, “Gradient-based identification methods for Hammerstein nonlinear ARMAX models,” Nonlinear Dynamics, vol. 45, no. 1-2, pp. 31–43, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. F. Ding, T. Chen, and Z. Iwai, “Adaptive digital control of Hammerstein nonlinear systems with limited output sampling,” SIAM Journal on Control and Optimization, vol. 45, no. 6, pp. 2257–2276, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. 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
  13. J. Li, F. Ding, and G. Yang, “Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 442–450, 2012. View at Publisher · View at Google Scholar · View at Scopus
  14. F. Ding and T. Chen, “Identification of Hammerstein nonlinear ARMAX systems,” Automatica, vol. 41, no. 9, pp. 1479–1489, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. F. Ding, Y. Shi, and T. Chen, “Auxiliary model-based least-squares identification methods for Hammerstein output-error systems,” Systems & Control Letters, vol. 56, no. 5, pp. 373–380, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. D. Wang and F. Ding, “Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3157–3164, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. D. Wang, Y. Chu, G. Yang, and F. Ding, “Auxiliary model based recursive generalized least squares parameter estimation for Hammerstein OEAR systems,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 309–317, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. D. Wang, Y. Chu, and F. Ding, “Auxiliary model-based RELS and MI-ELS algorithm for Hammerstein OEMA systems,” Computers & Mathematics with Applications, vol. 59, no. 9, pp. 3092–3098, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. 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 · View at Scopus
  20. D. Wang and F. Ding, “Least squares based and gradient based iterative identification for Wiener nonlinear systems,” Signal Processing, vol. 91, no. 5, pp. 1182–1189, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. W. Fan, F. Ding, and Y. Shi, “Parameter estimation for Hammerstein nonlinear controlled auto-regression models,” in Proceedings of the IEEE International Conference on Automation and Logistics, pp. 1007–1012, Jinan, China, August 2007.
  22. L. Wang, F. Ding, and P. X. Liu, “Convergence of HLS estimation algorithms for multivariable ARX-like systems,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1081–1093, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, NJ, USA, 1984.
  24. Y. Liu, L. Yu, and F. Ding, “Multi-innovation extended stochastic gradient algorithm and its performance analysis,” Circuits, Systems, and Signal Processing, vol. 29, no. 4, pp. 649–667, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. F. Ding and T. Chen, “Combined parameter and output estimation of dual-rate systems using an auxiliary model,” Automatica, vol. 40, no. 10, p. 1739, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. F. Ding and T. Chen, “Performance analysis of multi-innovation gradient type identification methods,” Automatica, vol. 43, no. 1, pp. 1–14, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. L. Han and F. Ding, “Multi-innovation stochastic gradient algorithms for multi-input multi-output systems,” Digital Signal Processing, vol. 19, no. 4, pp. 545–554, 2009. View at Publisher · View at Google Scholar · View at Scopus
  28. F. Ding, “Several multi-innovation identification methods,” Digital Signal Processing, vol. 20, no. 4, pp. 1027–1039, 2010. View at Google Scholar
  29. D. Wang and F. Ding, “Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems,” Digital Signal Processing, vol. 20, no. 3, pp. 750–762, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. J. Zhang, F. Ding, and Y. Shi, “Self-tuning control based on multi-innovation stochastic gradient parameter estimation,” Systems & Control Letters, vol. 58, no. 1, pp. 69–75, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  31. F. Ding, H. Chen, and M. Li, “Multi-innovation least squares identification methods based on the auxiliary model for MISO systems,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 658–668, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  32. L. Xie, Y. J. Liu, H. Z. Yang, and F. Ding, “Modelling and identification for non-uniformly periodically sampled-data systems,” IET Control Theory & Applications, vol. 4, no. 5, pp. 784–794, 2010. View at Publisher · View at Google Scholar
  33. F. Ding, P. X. Liu, and G. Liu, “Multiinnovation least-squares identification for system modeling,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 40, no. 3, Article ID 5299173, pp. 767–778, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. J. Ding, Y. Shi, H. Wang, and F. Ding, “A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems,” Digital Signal Processing, vol. 20, no. 4, pp. 1238–1247, 2010. View at Publisher · View at Google Scholar · View at Scopus
  35. F. Ding, P. X. Liu, and H. Yang, “Parameter identification and intersample output estimation for dual-rate systems,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 38, no. 4, pp. 966–975, 2008. View at Publisher · View at Google Scholar · View at Scopus
  36. Y. Liu, D. Wang, and F. Ding, “Least squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data,” Digital Signal Processing, vol. 20, no. 5, pp. 1458–1467, 2010. View at Publisher · View at Google Scholar · View at Scopus
  37. D. Wang and F. Ding, “Input-output data filtering based recursive least squares identification for CARARMA systems,” Digital Signal Processing, vol. 20, no. 4, pp. 991–999, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. F. Ding, P. X. Liu, and G. Liu, “Gradient based and least-squares based iterative identification methods for OE and OEMA systems,” Digital Signal Processing, vol. 20, no. 3, pp. 664–677, 2010. View at Publisher · View at Google Scholar · View at Scopus
  39. D. Wang, G. Yang, and R. Ding, “Gradient-based iterative parameter estimation for Box-Jenkins systems,” Computers & Mathematics with Applications, vol. 60, no. 5, pp. 1200–1208, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  40. L. Xie, H. Yang, and F. Ding, “Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 315–324, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  41. F. Ding, Y. Liu, and B. Bao, “Gradient-based and least-squares-based iterative estimation algorithms for multi-input multi-output systems,” Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, vol. 226, no. 1, pp. 43–55, 2012. View at Publisher · View at Google Scholar · View at Scopus
  42. F. Ding, “Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling,” Applied Mathematical Modelling. In press. View at Publisher · View at Google Scholar
  43. F. Ding and J. Ding, “Least-squares parameter estimation for systems with irregularly missing data,” International Journal of Adaptive Control and Signal Processing, vol. 24, no. 7, pp. 540–553, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  44. Y. Liu, L. Xie, and F. Ding, “An auxiliary model based on a recursive least-squares parameter estimation algorithm for non-uniformly sampled multirate systems,” Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, vol. 223, no. 4, pp. 445–454, 2009. View at Publisher · View at Google Scholar · View at Scopus
  45. F. Ding, L. Qiu, and T. Chen, “Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems,” Automatica, vol. 45, no. 2, pp. 324–332, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  46. F. Ding, G. Liu, and X. P. Liu, “Partially coupled stochastic gradient identification methods for non-uniformly sampled systems,” IEEE Transactions on Automatic Control, vol. 55, no. 8, pp. 1976–1981, 2010. View at Publisher · View at Google Scholar
  47. J. Ding and F. Ding, “Bias compensation-based parameter estimation for output error moving average systems,” International Journal of Adaptive Control and Signal Processing, vol. 25, no. 12, pp. 1100–1111, 2011. View at Publisher · View at Google Scholar · View at Scopus
  48. F. Ding and T. Chen, “Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite meaurement data,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 52, no. 3, pp. 555–566, 2005. View at Publisher · View at Google Scholar
  49. F. Ding and T. Chen, “Hierarchical identification of lifted state-space models for general dual-rate systems,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 52, no. 6, pp. 1179–1187, 2005. View at Publisher · View at Google Scholar