Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control

Ruiyun Qi; Mietek A. Brdys

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 4, page 619-630
  • ISSN: 1641-876X

Abstract

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In this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzy model is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and the parameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation (RLSE) algorithm. The rules of the fuzzy model can be added, replaced or deleted on-line to allow a more flexible and compact model structure. The overall controller consists of an indirect adaptive controller and a supervisory controller. The former is the dominant controller, which maintains the closed-loop stability when the fuzzy system is a good approximation of the nonlinear plant. The latter is an auxiliary controller, which is activated when the tracking error reaches the boundary of a predefined constraint set. It is proven that global stability of the closed-loop system is guaranteed in the sense that all the closed-loop signals are bounded and simulation examples demonstrate the effectiveness of the proposed control scheme.

How to cite

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Ruiyun Qi, and Mietek A. Brdys. "Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control." International Journal of Applied Mathematics and Computer Science 19.4 (2009): 619-630. <http://eudml.org/doc/207960>.

@article{RuiyunQi2009,
abstract = {In this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzy model is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and the parameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation (RLSE) algorithm. The rules of the fuzzy model can be added, replaced or deleted on-line to allow a more flexible and compact model structure. The overall controller consists of an indirect adaptive controller and a supervisory controller. The former is the dominant controller, which maintains the closed-loop stability when the fuzzy system is a good approximation of the nonlinear plant. The latter is an auxiliary controller, which is activated when the tracking error reaches the boundary of a predefined constraint set. It is proven that global stability of the closed-loop system is guaranteed in the sense that all the closed-loop signals are bounded and simulation examples demonstrate the effectiveness of the proposed control scheme.},
author = {Ruiyun Qi, Mietek A. Brdys},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fuzzy control; self-structuring fuzzy model; on-line modeling; stability},
language = {eng},
number = {4},
pages = {619-630},
title = {Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control},
url = {http://eudml.org/doc/207960},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Ruiyun Qi
AU - Mietek A. Brdys
TI - Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 4
SP - 619
EP - 630
AB - In this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzy model is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and the parameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation (RLSE) algorithm. The rules of the fuzzy model can be added, replaced or deleted on-line to allow a more flexible and compact model structure. The overall controller consists of an indirect adaptive controller and a supervisory controller. The former is the dominant controller, which maintains the closed-loop stability when the fuzzy system is a good approximation of the nonlinear plant. The latter is an auxiliary controller, which is activated when the tracking error reaches the boundary of a predefined constraint set. It is proven that global stability of the closed-loop system is guaranteed in the sense that all the closed-loop signals are bounded and simulation examples demonstrate the effectiveness of the proposed control scheme.
LA - eng
KW - fuzzy control; self-structuring fuzzy model; on-line modeling; stability
UR - http://eudml.org/doc/207960
ER -

References

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  9. Hao, Y., Y. D.-S. L. and Shao, S. (1999). Comparison of necessary conditions for typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators, IEEE Transactions on System, Man and Cybernetics-Part B: Cybernetics 29(5): 508-514. 
  10. Ogata, K. (1995). Discrete-time Control System, 2nd Ed., Prentice-Hall, Upper Saddle River, NJ. 
  11. Park, C.-W. and Cho, Y.-W. (2004). T-S model based indirect adaptive fuzzy control using online parameter estimation, IEEE Transactions on System, Man and Cybernetics-Part B: Cybernetics 34(6): 2293-2302. 
  12. Phan, P. A. and Gale, T. J. (2008). Direct adaptive fuzzy control with a self-structuring algorithm, Fuzzy Sets and Systems 159(8): 871-899. Zbl1170.93345
  13. Qi, R. and Brdys, M. A. (2008). Stable indirect adaptive control based on discrete-time T-S fuzzy model, Fuzzy Sets and Systems 159(8): 900-925. Zbl1170.93347
  14. Wang, L. (1994). Adaptive Fuzzy System and Control: Design and Stability Analysis, Prentice-Hall, Englewood Cliffs, NJ. 

Citations in EuDML Documents

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  1. Tomasz Zubowicz, Mietek A. Brdyś, Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case
  2. Mietek A. Brdyś, Marcin T. Brdyś, Sebastian M. Maciejewski, Adaptive predictions of the euro/złoty currency exchange rate using state space wavelet networks and forecast combinations
  3. Shaocheng Tong, Changliang Liu, Yongming Li, Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systems
  4. Moêz Soltani, Abdelkader Chaari, Fayçal Ben Hmida, A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

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