Table of Contents Author Guidelines Submit a Manuscript
Journal of Control Science and Engineering
Volume 2016 (2016), Article ID 9614167, 12 pages
http://dx.doi.org/10.1155/2016/9614167
Research Article

Combined Parameter and State Estimation Algorithms for Multivariable Nonlinear Systems Using MIMO Wiener Models

University of Sfax, National Engineering School of Sfax (ENIS), Laboratory of Sciences and Technique of Automatic Control and Computer Engineering (Lab-SAT), BP 1173, 3038 Sfax, Tunisia

Received 29 November 2015; Revised 20 April 2016; Accepted 12 May 2016

Academic Editor: James Lam

Copyright © 2016 Houda Salhi and Samira Kamoun. 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. H. Han, L. Xie, F. Ding, and X. Liu, “Hierarchical least-squares based iterative identification for multivariable systems with moving average noises,” Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1213–1220, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. R. Q. Fuentes, I. Chairez, A. Poznyak, and T. Poznyak, “3D nonparametric neural identification,” Journal of Control Science and Engineering, vol. 2012, Article ID 618403, 10 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  3. 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 MathSciNet · View at Scopus
  4. Y. Liu, F. Ding, and Y. Shi, “An efficient hierarchical identification method for general dual-rate sampled-data systems,” Automatica, vol. 50, no. 3, pp. 962–970, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. A. Fathi and A. Mozaffari, “Identification of a dynamic model for shape memory alloy actuator using Hammerstein-Wiener gray box and mutable smart bee algorithm,” International Journal of Intelligent Computing and Cybernetics, vol. 6, no. 4, pp. 328–357, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. A. D. Kalafatis, L. Wang, and W. R. Cluett, “Linearizing feedforward-feedback control of pH processes based on the Wiener model,” Journal of Process Control, vol. 15, no. 1, pp. 103–112, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Bhattacharjee and A. Sutradhar, “Online identification and internal model control for regulating hemodynamic variables in congestive heart failure patient,” International Journal of Pharma Medicine and Biological Sciences, vol. 4, no. 2, pp. 85–89, 2015. View at Google Scholar
  8. Y. Mao and F. Ding, “Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique,” Nonlinear Dynamics, vol. 79, no. 3, pp. 1745–1755, 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. W. Yu, D. Wilson, and B. Young, “Control performance assessment for block-oriented nonlinear systems,” in Proceedings of the 8th IEEE International Conference on Control and Automation (ICCA '10), pp. 1151–1156, Xiamen, China, June 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. S. I. Biagiola and J. L. Figueroa, “Wiener and Hammerstein uncertain models identification,” Mathematics and Computers in Simulation, vol. 79, no. 11, pp. 3296–3313, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. F. Guo, A new identification method for wiener and hammerstein systems [Ph.D. thesis], Karlsruhe University, 2004.
  12. M. Salimifard, M. Jafari, and M. Dehghani, “Identification of nonlinear MIMO block-oriented systems with moving average noises using gradient based and least squares based iterative algorithms,” Neurocomputing, vol. 94, pp. 22–31, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. H. Salhi, S. Kamoun, N. Essounbouli, and A. Hamzaoui, “Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models,” International Journal of Control, vol. 89, no. 3, pp. 611–622, 2016. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. H. Salhi and S. Kamoun, “A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models,” Applied Mathematical Modelling Journal, vol. 39, no. 16, pp. 4951–4962, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. H. Salhi and S. Kamoun, “State and parametric estimation of nonlinear systems described by wiener sate-space mathematical models,” in Handbook of Research on Advanced Intelligent Control Engineering and Automation, chapter 4, pp. 107–147, 2014. View at Publisher · View at Google Scholar
  16. S. I. Biagiola and J. L. Figueroa, “Identification of uncertain MIMO Wiener and Hammerstein models,” Computers and Chemical Engineering, vol. 35, no. 12, pp. 2867–2875, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Lakshminarayanan, S. L. Shah, and K. Nandakumar, “Identification of Hammerstein models using multivariate statistical tools,” Chemical Engineering Science, vol. 50, no. 22, pp. 3599–3613, 1995. View at Publisher · View at Google Scholar · View at Scopus
  18. F. Ding, “Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling,” Applied Mathematical Modelling, vol. 37, no. 4, pp. 1694–1704, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. Z. Zhang, F. Ding, and X. Liu, “Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems,” Computers & Mathematics with Applications, vol. 61, no. 3, pp. 672–682, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. J. Vörös, “Iterative identification of nonlinear dynamic systems with output backlash using three-block cascade models,” Nonlinear Dynamics, vol. 79, no. 3, pp. 2187–2195, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Y. Hu, B. Liu, Q. Zhou, and C. Yang, “Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises,” Circuits, Systems, and Signal Processing, vol. 33, no. 2, pp. 655–664, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. F. Ding, X. G. Liu, and J. Chu, “Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle,” IET Control Theory & Applications, vol. 7, no. 2, pp. 176–184, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. J. H. Li, “Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration,” Applied Mathematics Letters, vol. 26, no. 1, pp. 91–96, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. F. Guo and G. Bretthauer, “Identification of MISO Wiener and Hammerstein systems,” in Proceedings of the 7th European Control Conference (TEE '03), pp. 2144–2149, University of Cambridge, September 2003. View at Scopus
  25. N. I. Chaudhary, M. A. Z. Raja, J. A. Khan, and M. S. Aslam, “Identification of input nonlinear control autoregressive systems using fractional signal processing approach,” The Scientific World Journal, vol. 2013, Article ID 467276, 13 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  26. Z. Wu, S. Peng, B. Chen, and H. Zhao, “Robust Hammerstein adaptive filtering under maximum correntropy criterion,” Entropy, vol. 17, no. 10, pp. 7149–7166, 2015. View at Google Scholar · View at MathSciNet
  27. T. Falck, P. Dreesen, K. De Brabanter, K. Pelckmans, B. De Moor, and J. A. K. Suykens, “Least-squares support vector machines for the identification of Wiener-Hammerstein systems,” Control Engineering Practice, vol. 20, no. 11, pp. 1165–1174, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. A. Y. Kibangou and G. Favier, “Identification of parallel-cascade Wiener systems using joint diagonalization of third-order Volterra kernel slices,” IEEE Signal Processing Letters, vol. 16, no. 3, pp. 188–191, 2009. View at Publisher · View at Google Scholar · View at Scopus
  29. A. Y. Kibangou and G. Favier, “Tensor analysis-based model structure determination and parameter estimation for block-oriented nonlinear systems,” IEEE Journal on Selected Topics in Signal Processing, vol. 4, no. 3, pp. 514–525, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. X. Wang and F. Ding, “Modelling and multi-innovation parameter identification for Hammerstein nonlinear state space systems using the filtering technique,” Mathematical and Computer Modelling of Dynamical Systems, vol. 22, no. 2, pp. 113–140, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  31. F. Ding, X. Liu, and X. Ma, “Kalman state filtering based least squares iterative parameter estimation for observer canonical state space systems using decomposition,” Journal of Computational and Applied Mathematics, vol. 301, pp. 135–143, 2016. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. F. Ding, “Combined state and least squares parameter estimation algorithms for dynamic systems,” Applied Mathematical Modelling, vol. 38, no. 1, pp. 403–412, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. X. Ma and F. Ding, “Gradient-based parameter identification algorithms for observer canonical state space systems using state estimates,” Circuits, Systems, and Signal Processing, vol. 34, no. 5, pp. 1697–1709, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. 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 · View at MathSciNet · View at Scopus
  35. X. Ma and F. Ding, “Recursive and iterative least squares parameter estimation algorithms for observability canonical state space systems,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 352, no. 1, pp. 248–258, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  36. X. Wang and F. Ding, “Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle,” Signal Processing, vol. 117, pp. 208–218, 2015. View at Publisher · View at Google Scholar · View at Scopus
  37. D.-Q. Wang and F. Ding, “Hierarchical least squares estimation algorithm for hammerstein-wiener systems,” IEEE Signal Processing Letters, vol. 19, no. 12, pp. 825–828, 2012. View at Publisher · View at Google Scholar · View at Scopus
  38. D. Wang, F. Ding, and L. Ximei, “Least squares algorithm for an input nonlinear system with a dynamic subspace state space model,” Nonlinear Dynamics, vol. 75, no. 1-2, pp. 49–61, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. D. Westwick and M. Verhaegen, “Identifying MIMO Wiener systems using subspace model identification methods,” Signal Processing, vol. 52, no. 2, pp. 235–258, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  40. J. Bruls, C. T. Chou, B. R. J. Haverkamp, and M. Verhaegen, “Linear and non-linear system identification using separable least-squares,” European Journal of Control, vol. 5, no. 1, pp. 116–128, 1999. View at Publisher · View at Google Scholar · View at Scopus
  41. M. Lovera, T. Gustafsson, and M. Verhaegen, “Recursive subspace identification of linear and non-linear Wiener state-space models,” Automatica, vol. 36, no. 11, pp. 1639–1650, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. T. Á. Glaria Lopez and D. Sbarbaro, “Observer design for nonlinear processes with Wiener structure,” in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC '11), pp. 2311–2316, IEEE, Orlando, Fla, USA, December 2011. View at Publisher · View at Google Scholar · View at Scopus
  43. E.-W. Bai, “Identification of linear systems with hard input nonlinearities of known structure,” Automatica, vol. 38, no. 5, pp. 853–860, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. J. Vörös, “Parameter identification of Wiener systems with discontinuous nonlinearities,” Systems and Control Letters, vol. 44, no. 5, pp. 363–372, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  45. K. Xiong, C. L. Wei, and L. D. Liu, “Robust Kalman filtering for discrete-time nonlinear systems with parameter uncertainties,” Aerospace Science and Technology, vol. 18, no. 1, pp. 15–24, 2012. View at Publisher · View at Google Scholar · View at Scopus