Adaptive Controller for T-S Fuzzy Model with Modeling Error

Hugang Han

doi:10.20965/jaciii.2011.p0759

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JACIII Vol.15 No.7 pp. 759-766

doi: 10.20965/jaciii.2011.p0759

(2011)

Paper:

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Adaptive Controller for T-S Fuzzy Model with Modeling Error

Hugang Han

Faculty of Management and Information Systems, Prefectural University of Hiroshima, 1-1-71 Ujina-higashi, Minami-ku, Hiroshima, Hiroshima 734-8558, Japan

Received:

March 15, 2011

Accepted:

April 25, 2011

Published:

September 20, 2011

Keywords:

T-S fuzzy model, modeling error, adaptive control, LMIs

Abstract

Modeling error occurs in linearizing the real (nonlinear) system into the (linear) T-S fuzzy model, and the existence of uncertainties in the real system including external disturbances. This paper deals with the T-S fuzzy model with modeling error in order to improve the control performance. As a result, an adaptive controller that consists of two parts: one is obtained by solving certain Linear Matrix Inequalities (LMIs) (fixed part) and the other is acquired by the fuzzy approximator in which the related parameters are tuned by adaptive law (variable part), is proposed. The proposed controller can guarantee all signals involved in the closed-loop system uniformly ultimately bounded.

Cite this article as:

H. Han, “Adaptive Controller for T-S Fuzzy Model with Modeling Error,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.7, pp. 759-766, 2011.

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References

[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] M. Sugeno and G. T. Kang, “Structure identification of fuzzy model,” Fuzzy Sets Syst., Vol.28, No.10, pp. 15-33, 1988.
[3] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets Syst., Vol.45, No.2, pp. 135-156, 1992.
[4] 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.
[5] 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.
[6] 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.
[7] F. Zheng, 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.
[8] 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.
[9] 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.
[10] H. Han, C.-Y. Su, and Y. Stepanenko, “Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators,” IEEE Trans. on Fuzzy Systems, Vol.9, No.2, pp. 315-323, 2001.
[11] H. Han, “Adaptive controller for T-S fuzzy model with reconstruction error,” IEEJ Trans. EIS, Vol.131, No.2, pp. 329-336, 2011.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[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] M. Sugeno and G. T. Kang, “Structure identification of fuzzy model,” Fuzzy Sets Syst., Vol.28, No.10, pp. 15-33, 1988.

[3] [3] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets Syst., Vol.45, No.2, pp. 135-156, 1992.

[4] [4] 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.

[5] [5] 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.

[6] [6] 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.

[7] [7] F. Zheng, 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.

[8] [8] 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.

[9] [9] 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.

[10] [10] H. Han, C.-Y. Su, and Y. Stepanenko, “Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators,” IEEE Trans. on Fuzzy Systems, Vol.9, No.2, pp. 315-323, 2001.

[11] [11] H. Han, “Adaptive controller for T-S fuzzy model with reconstruction error,” IEEJ Trans. EIS, Vol.131, No.2, pp. 329-336, 2011.