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JACIII Vol.18 No.6 pp. 908-917
doi: 10.20965/jaciii.2014.p0908
(2014)

Paper:

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Discrete Sliding-Mode Control for a Class of T-S Fuzzy Models with Modeling Error

Hugang Han* and Hak-Keung Lam**

*Prefectural University of Hiroshima, 1-1-71 Ujina-Higashi, Minami-ku, Hiroshima 734-8558, Japan

**King’s College London, Strand, London, WC2R 2LS, UK

Received:
April 18, 2014
Accepted:
August 6, 2014
Published:
November 20, 2014
Creative Commons License
Keywords:
adaptive control, discrete nonlinear systems, fuzzy approximator, sliding mode control, stability analysis
Abstract
This paper proposes a discrete sliding-mode controller for a class of nonlinear systems described by a T-S fuzzy model subject to modeling error, which may influence the system performance and the overall system stability. While most of existing literature treats the modeling error under the so-called parallel distributed compensation framework by using some norm-bounded matrices, the proposed control scheme in this paper integrates a feedback component, which mainly consists of fuzzy approximators to deal with the modeling error and an auxiliary component of the variable structure control with a sector to guarantee the global stability of the closed-loop system when the system state travels outside the sector. With the consideration of system stability, adaptive laws adjusting the parameters in the system are developed based on the Lyapunov synthesis approach. Finally, simulation results will confirm the effectiveness of the approach proposed in this paper.
Cite this article as:
H. Han and H. Lam, “Discrete Sliding-Mode Control for a Class of T-S Fuzzy Models with Modeling Error,” J. Adv. Comput. Intell. Intell. Inform., Vol.18 No.6, pp. 908-917, 2014.
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References
  1. [1] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., Vol.15, pp. 116-132, 1985.
  2. [2] K. Tanaka and H. O. Wang, “Fuzzy control systems design and analysis: A linear matrix inequality approach,” Wiley-Interscience, 2004.
  3. [3] G. Feng, “A survey on analysis and design of model-based fuzzy control systems,” IEEE Trans. Fuzzy Syst., Vol.14, pp. 676-697, 2006.
  4. [4] A. Sala and C. Ariño, “Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya’s theorem,” Fuzzy Sets and Systems, Vol.158, No.24, pp. 2671-2686, 2007.
  5. [5] H. K. Lam and M. Narimani, “Stability analysis and performance deign for fuzzy-model-based control system under imperfect premise matching,” IEEE Trans. Fuzzy Sys., Vol.17, No.4, pp. 949-961, 2009.
  6. [6] H. K. Lam, “LMI-based stability analysis for fuzzy-model-based control systems using artificial T-S fuzzy model,” IEEE Trans. Fuzzy Sys., Vol.19, No.3, pp. 505-513, 2011.
  7. [7] H. K. Lam and J. Lauber, “Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions,” Information Sciences, Vol.232, pp. 253-266, 2013.
  8. [8] K. Tanaka, T. Ikeda, and H. O. Wang, “Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H∞ control theory, and linear matrix inequalities,” IEEE Trans. Fuzzy Syst., Vol.4, pp. 1-13, 1996.
  9. [9] Y.-Y Cao and Z. Lin, “Robust stability analysis and fuzzyscheduling control for nonlinear systems subject to actuator saturation,” IEEE Trans. Fuzzy Syst., Vol.11, No.1, pp. 57-67, 2003.
  10. [10] B. Chen, X. Liu, S. Tong, and C. Lin, “Guaranteed cost control of T-S fuzzy systems with state and input delays,” Fuzzy Sets Syst., Vol.158, pp. 2251-2267, 2007.
  11. [11] F. Zhang, Q.-G. Wang, and T. H. Lee, “Adaptive and robust controller design for uncertain nonlinear systems via fuzzy modeling approach,” IEEE Trans. Syst., Man, and Cybern. Vol.34, No.1, pp. 166-178, 2004.
  12. [12] H. Han, “Adaptive fuzzy controller for a class of uncertain nonlinear systems,” J. of Japan Society for Fuzzy Theory and Intelligence Informatics, Vol.21, No.4, pp. 577-586, 2009.
  13. [13] H. Han and T. Koshiro, “Adaptive T-S fuzzy controller using fuzzy approximators,” Proc. of 2010 IEEE World Congress on Computational Intelligence, Barcelona, Spain, 2010.
  14. [14] H. Han, “Adaptive controller for T-S fuzzy model with reconstruction error,” IEEJ Trans. EIS, Vol.131, No.2, pp. 329-336, 2011.
  15. [15] R.-J. Wai and Z.-W. Yang, “Adaptive fuzzy neural network control design via a T-S fuzzy model for a robot manipulator including actuator dynamics,” Trans. Syst., Man, Cybern. B, Cybern., Vol.38, No.5, pp. 1326-1346, 2008.
  16. [16] Y.-H. Chang, W.-S. Chan, and C.-W. Chang, “T-S fuzzy modelbased adaptive dynamic surface control for ball and beam system,” IEEE Trans. Ind. Electron., Vol.60, No.0, pp. 2251-2263, 2013.
  17. [17] H. Li, J. Yu, C. Hilton, and H. Liu, “Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach,” IEEE Trans. Ind. Electron., Vol.60, No.8, pp. 3328-3338, 2013.
  18. [18] C.-W. Park and Y.-W. Cho, “T-S model based indirect adaptive fuzzy control using online parameter estimation,” IEEE Trans. Syst., Man, Cybern. B, Cybern., Vol.34, No.6, pp. 2293-2302, 2004.
  19. [19] C. Hua, Q.-G. Wang, and X. Guan, “Robust adaptive controller design for nonlinear time-delay systems via T-S fuzzy approach,” IEEE Trans. Fuzzy Sys., Vol.17, No.4, pp. 901-910, 2009.
  20. [20] M. A. Khanesar, O. Kaynak, and M. Teshnehlab, “Direct model reference Takagi-Sugeno fuzzy control of SISO nonlinear systems,” IEEE Trans. Fuzzy Sys., Vol.19, No.5, pp. 914-924, 2011.
  21. [21] T. V. Dang, W.-J. Wang, L. Luoh, and C.-H. Sun, “Adaptive observer design for the uncertain Takagi-Sugeno fuzzy system with output disturbance,” IET Con. Theory & App., Vol. 6, No.10, pp. 1351-1366, 2012.
  22. [22] R. Qi, G. Tao, B. Jiang, and C. Tan, “Adaptive control schemes for discrete-time T-S fuzzy systems with unknown parameters and actuator failures,” IEEE Trans. Fuzzy Sys., Vol.30, No.3, pp. 471-486, 2012.
  23. [23] C. Edwards and S. K. Spurgeon, “Sliding Mode Control: Theory and Applications,” New York: Taylor & Francis, 1998.
  24. [24] J. Yang, Q. Wang, and Y. Li, “Stabilization of an under actuated ball-and-beam system using a second-order sliding mode control,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.18, No.2, pp. 121-127, 2014.
  25. [25] P. C. Chen, C.-W. Chen, and W. L. Chiang, “GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.9, No.2, pp. 100-105, 2005.
  26. [26] K. Yeh and W.-L. Chiang, “Application of adaptive fuzzy sliding mode control for bridges,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.5, No.3, pp. 172-179, 2001.
  27. [27] F. Zheng, Q.-G. Wang, and T. H. Lee, “Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach,” IEEE Trans. Fuzzy Sys., Vol.10, No.6, pp. 686-697, 2002.
  28. [28] D. W. C. Ho, and Y. Niu, “Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control,” IEEE Trans. Fuzzy Sys., Vol.15, No.3, pp. 350-358, 2007.
  29. [29] Y. Hacioglu, Y. Z. Arslan, and N. Yagiz, “MIMO fuzzy sliding mode controlled dual arm robot in load transportation,” J. of the Franklin Institute, Vol.348, No.8, pp. 1886-1902, 2011.
  30. [30] C. Han, G. Zhang, L. Wu, and Q. Zeng, “Sliding mode control of T-S fuzzy descriptor systems with time-delay,” J. of the Franklin Institute, Vol.349, No.4, pp. 1430-1444, 2013.
  31. [31] C. Lin, Q.-G.Wang, and T. H. Lee, “Stabilization of uncertain fuzzy time-delay systems via variable structure control approach,” IEEE Trans. Fuzzy Sys., Vol.13, No.6, pp. 787-798, 2005.
  32. [32] D. W. C. Ho, and Y. Niu, “Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control,” IEEE Trans. Fuzzy Sys., Vol.15, No.3, pp. 350-358, 2007.
  33. [33] J. Zhang, P. Shi, and Y. Xia, “Robust adaptive sliding-mode control for fuzzy systems with mismatched uncertainties,” IEEE Trans. Fuzzy Sys., Vol.18, No.4, pp. 700-711, 2010.
  34. [34] H. H. Choi, “Robust stabilization of uncertain fuzzy-time-delay systems using sliding-mode-control approach,” IEEE Trans. Fuzzy Sys., Vol.18, No.5, pp. 979-984, 2010.
  35. [35] K. Furuta, “VSS type self-tuning control,” IEEE Trans. Ind. Electron., Vol.40, No.1, pp. 37-44, 1993.
  36. [36] H. Han and S. Murakami, “A design for a class of nonlinear systems with delay time using fuzzy logic,” Soft Computing, Vol.7, No.4, pp. 251-257, 2003.
  37. [37] L.-X. Wang, “Stable adaptive fuzzy control of nonlinear system,” IEEE Trans. Fuzzy Sys., Vol.1, pp. 146-155, 1993.
  38. [38] L.-X. Wang and J. M. Mendal, “Fuzzy basis functions, universal approximation, and orthogonal least-squares learning” IEEE Trans. Neural Networks, Vol.3, pp. 807-814, 1992.
  39. [39] H. Han, C.-Y. Su, and Y. Stepanenko, “Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators,” IEEE Trans. Fuzzy Sys., Vol.9, No.2, pp. 315-323, 2001.
  40. [40] H. Han and T. Tanaka, “A time-delay-dependent approach for a class of T-S fuzzy models with time delays and uncertainties,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.16, No.6, pp. 748-757, 2012.
  41. [41] Y.-Y. Cao and P.M. Frank, “Robust H∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems,” IEEE Trans. Fuzzy Sys., Vol.8, No.4, pp. 406-415, 2000.

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