A Type-2 Fuzzy Adaptive Controller of a Class of Nonlinear System

In this paper we propose a robust adaptive fuzzy controller for a class of nonlinear system with unknown dynamic. The method is based on type-2 fuzzy logic system to approximate unknown non-linear function. The design of the on-line adaptive scheme of the proposed controller is based on Lyapunov technique. Simulation results are given to illustrate the effectiveness of the proposed approach.

Authors:

• A. El Ougli
• I. Lagrat
• I. Boumhidi

Keywords:

• Fuzzy set type-2
• Adaptive fuzzy control
• Nonlinear system.

References:

[1] J. E. Slotine, W. P. Li, Applied Nonlinear Control. Prentice Hall, 1991.
[2] T. Takagi, M. Sugeno, "Fuzzy Identification of Systems and its
Application to Modelling and Control," IEEE Trans. Systems, Man and
Cybernetics, 15 (1), pp. 116-132, 1985.
[3] G. Feng, "Analysis of a new algorithm for continuous time robust
adaptive control," IEEE Trans. Automatic Control, vol. 44, no. 9, pp.
1764-1768, sep 1999.
[4] R. Babuska, Fuzzy Modelling for Control, Kluwer Academic Publishers,
Boston, 1998.
[5] G. Feng, G. Chen, "Adaptive control of discret-time chaotic systems: a
fuzzy control approach," Chaos. Solutions and Fractals 23, pp. 459-467,
2005.
[6] J. M. Mendel, "Computing Derivatives in Interval Type-2 Fuzzy logic
Systems," IEEE Trans. Fuzzy Systems, vol. 12, no.1, pp.84-98, Feb.
2004.
[7] J. S. Wang, C. S. G. Lee, "Sel-Adaptive Neuro-Fuzzy Inference Systems
For Classification Application,", IEEE Trans. Fuzzy Systems, vol. 10,
no. 6, pp. 790-802, 2002.
[8] Z. Kovacic, M. Balenovic, S. Bogdan, "Sensitivity based self learning
fuzzy logic control for a servo system," IEEE Control Systems. June
1998.
[9] N. Golea, A. Golea, K. Benmahammed, "Fuzzy Model Reference
Adaptive Control," Fuzzy Sets and Systems, 137 (3), pp. 353-366, 2003.
[10] M. Hojati, S. Gazor, "Hybrid Adaptive Fuzzy Identification and Control
of Nonlinear Systems," IEEE Trans. Fuzzy Systems, vol. 10, no. .2, pp.
198-210, 2002.
[11] H. Lee, M. Tomizuka, "Robust Adaptive Control using a Universal
Approximator for SISO Nonlinear Systems," IEEE Trans. Fuzzy
Systems, vol. .8, pp. .95-106, 2001.
[12] C. H. Wang, C. S. Lee, "Dynamical Optimal Training for Interval Type-
2 Fuzzy Neural Network (T2FNN)," IEEE Trans. Systems, Man and
Cybernetics. Part B, vol.. 34, no. .3, pp.1462-1477, 2004.
[13] J. M. Mendel, Rule-Based Fuzzy Logic Systems: Introduction and New
Directions. Prentice Hall, Englewood Cliffs, NJ.