Advertisement

Fuzzy H Filter Design for Nonlinear Discrete-Time Systems with Multiple Time-Delays

Part of the Control Engineering book series (CONTRENGIN)

Abstract

The problem of robust H filtering for systems with uncertain external disturbances and measurement noises has been of great interests [7, 18, 21]. The advantage of using an H filter over a Kalman filter is that no statistical assumption about the noise signals is required. In robust H filtering, the noise signals are assumed to be arbitrary with bounded energy (or average power). H filters are designed by minimizing signal estimation errors for bounded disturbances and noises of the worst case. Thus, H filters are more robust than Kalman filters. Moreover, the H filtering approach provides both a guaranteed noise attention level and a strong robustness against unmodeled dynamics.

Keywords

IEEE Transaction Fuzzy System Linear Matrix Inequality Fuzzy Model Extended Kalman Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    B. Anderson and J. Moore, Optimal Filtering, Englewood Cliffs, NJ: Prentice Hall, 1979.MATHGoogle Scholar
  2. [2]
    P. Apkarian, H. D. Tuan, and J. Bernussou, “Continuous-time analysis, eigenstructure assignment, and H 2 synthesis with enhanced linear matrix inequalities (LMI) characterizations,” IEEE Transactions on Automatic Control, vol.46, pp. 1941–1946, Dec. 2001.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics, vol. 15, Philadelphia: SIAM, 1994.Google Scholar
  4. [4]
    C. Breining, “Control of a hands-free telephone set,” Signal Processing, vol.61, pp. 131–143, Sept. 1997.MATHCrossRefGoogle Scholar
  5. [5]
    B.-S. Chen, C.-L. Tsai, and D.-S. Chen, “Robust H and mixed H 2/H filters for equalization designs of nonlinear communication systems: Fuzzy interpolation approach,” IEEE Transactions on Fuzzy Systems, vol. 11, pp. 384–398, June 2003.CrossRefGoogle Scholar
  6. [6]
    C. E. de Souza, R. M. Palhares, and P. L. D. Peres, “Robust H filter design for uncertain linear systems with multiple time-varying state delays,” IEEE Transactions on Signal Processing, vol. 49, pp. 569–576, Mar. 2001.CrossRefMathSciNetGoogle Scholar
  7. [7]
    C. E. de Souza, U. Shaked, and M. Fu, “Robust H filtering for continuous time varying uncertain systems with deterministic input signals,” IEEE Transactions on Signal Processing, vol. 43, pp. 709–719, Mar. 1995.CrossRefGoogle Scholar
  8. [8]
    G. Feng, T. H. Lee, and N. Zhang, “Stable filter design of fuzzy dynamic systems,” Proceedings of the IEEE World Congress on Computational Intelligence, Anchorage, AK, May 1998, pp. 474–480.Google Scholar
  9. [9]
    E. Fridman and U. Shaked, “A new H filter design for linear time delay systems,” IEEE Transactions on Signal Processing, vol. 49, pp. 2839–2843, Nov. 2001.CrossRefMathSciNetGoogle Scholar
  10. [10]
    J. C. Geromel, J. Bernussou, G. Garcia, and M. C. de Oliveira, “H 2 and H robust filtering for discrete-time linear systems,” Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, Dec. 1998, pp. 632–637.Google Scholar
  11. [11]
    E. Gershon, U. Shaked, and I. Yaesh, “Robust H estimation of stationary discrete-time linear processes with stochastic uncertainties,” Systems & Control Letters, vol. 45, pp. 257–269, Apr. 2002.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    S. Ichitsubo, T. Furuno, T. Taga, and R. Kawasaki, “Multipath propagation model for line-of-sight street microcells in urban area,” IEEE Transactions on Vehicular Technology, vol. 49, pp. 422–427, Mar. 2000.CrossRefGoogle Scholar
  13. [13]
    K. R. Lee, J. H. Kim, E. T. Jeung, and H. B. Park, “Output feedback robust H control of uncertain fuzzy dynamic systems with time-varying delay,” IEEE Transactions on Fuzzy Systems, vol. 49, pp. 657–664, Dec. 2000.Google Scholar
  14. [14]
    K. R. Lee, J. S. Lee, D. C. Oh, and H. B. Park, “Fuzzy H filtering for nonlinear systems with time-varying delayed states,” International Journal of Control, Automation, and Systems, vol. 1, no. 2, pp. 99–105, 1999.Google Scholar
  15. [15]
    Q. Liang, J. M. Mendel, “Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters,” IEEE Transactions on Fuzzy Systems, vol. 8, pp. 551–563, Oct. 2000.CrossRefGoogle Scholar
  16. [16]
    M. Malek-Zavarei and M. Jamshidi, Time-Delay Systems: Analysis, Optimization and Applications, Amsterdam: North-Holland, 1987.MATHGoogle Scholar
  17. [17]
    S. Mascolo, “Congestion control in high-speed communication networks using the Smith principle,” Automatica, vol. 35, pp. 1921–1935, Dec. 1999MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    K. Nishiyama, “Robust estimation of a single complex sinusoid in white noise-H filtering approach,” IEEE Transactions on Signal Processing, vol. 47, pp. 2853–2856, Oct. 1999.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    R. M. Palhares, C. E. de Souza, and P. L. D. Peres, “Robust H filtering for uncertain discrete-time state-delayed systems,” IEEE Transactions on Signal Processing, vol. 49, pp. 1696–1703, Aug. 2001.CrossRefMathSciNetGoogle Scholar
  20. [20]
    A. W. Pila, U. Shaked, and C. E. de Souza, “H filtering for continuous-time linear systems with delay,” IEEE Transactions on Automatic Control, vol.44, pp. 1412–1417, July 1999.MATHCrossRefGoogle Scholar
  21. [21]
    U. Shaked and N. Berman, “H nonlinear filtering of discrete-time processes,” IEEE Transactions on Signal Processing, vol. 43, pp. 2205–2209, Sept. 1995.CrossRefGoogle Scholar
  22. [22]
    M. Sugeno and T. Yasukawa, “A fuzzy-logic-based approach to qualitative modeling,” IEEE Transactions on Fuzzy Systems, vol. 1, pp. 7–31, Feb. 1993.CrossRefGoogle Scholar
  23. [23]
    T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modelling and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, pp. 116–132, 1985.MATHGoogle Scholar
  24. [24]
    C.-S. Tseng and B.-S. Chen, “H fuzzy estimation for a class of nonlinear discrete-time dynamic system,” IEEE Transactions on Signal Processing, vol. 49, pp. 2605–2619, Nov. 2001.CrossRefGoogle Scholar
  25. [25]
    L.-X. Wang, “Fuzzy systems as nonlinear dynamic system identifiers—Part I: Design,” Proceedings of the 31 st IEEE Conference on Decision and Control, Tucson, AZ, Dec. 1992, pp. 897–902.Google Scholar
  26. [26]
    L.-X. Wang, A Course in Fuzzy Systems and Control, Upper Saddle River, NJ: Prentice Hall, 1997.MATHGoogle Scholar
  27. [27]
    Z. Wang, B. Huang, and H. Unbehauen, “Robust H observer design of linear state delayed systems with parametric uncertainty: The discrete-time case,” Automatica, vol. 35, pp. 1161–1167, June 1999.MATHCrossRefMathSciNetGoogle Scholar
  28. [28]
    L.-X. Wang and J. M. Mendel, “Fuzzy basis functions, universal approximation and orthogonal least squares learning,” IEEE Transactions on Neural Networks, vol. 3, pp. 807–814, Sept. 1992CrossRefGoogle Scholar
  29. [29]
    L.-X. Wang and J. M. Mendel, “Fuzzy adaptive filters, with application to nonlinear channel equalization,” IEEE Transactions on Fuzzy Systems, vol. 1, pp. 161–170, Aug. 1993.CrossRefGoogle Scholar
  30. [30]
    L. Xie, C. E. de Souza, and M. Fu, “H estimation for discrete-time linear uncertain systems,” International Journal of Robust and Nonlinear Control, vol. 1, no. 2, pp. 111–123, 1991.MATHCrossRefGoogle Scholar
  31. [31]
    S. Xu and T. Chen “Reduced-order H filtering for stochastic systems,” IEEE Transactions on Signal Processing, vol. 50, pp. 2998–3007, Dec. 2002.CrossRefMathSciNetGoogle Scholar
  32. [32]
    H. Zhang, L. Cai, and Z. Bien, “A fuzzy basis function vector-based multi-variable adaptive fuzzy controller for nonlinear systems,” IEEE Transactions on systems, Man, and Cybernetics—Part B: Cybernetics, vol. 30, pp. 210–217, 2000.CrossRefGoogle Scholar
  33. [33]
    H. Zhang and Y. Quan, “Modeling, identification and control of a class of nonlinear system,” IEEE Transactions on Fuzzy Systems, vol. 9, pp. 349–354, 2001.CrossRefGoogle Scholar
  34. [34]
    H. S. Zhang, L. Xie, and Y. C. Soh, “H deconvolution filtering, prediction, and smoothing: A Krein space polynomial systems approach,” IEEE Transactions on Signal Processing, vol. 48, pp. 888–892, Mar. 2000.MATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 2006

Personalised recommendations