A general and formal methodology to design stable nonlinear fuzzy control systems

IEEE Transactions on Fuzzy Systems

Volumn 17, Issue 5, 2009, Pages 1081-1091

  Márquez, José Manuel Andújar ^a   Piña, Antonio Javier Barragán ^a   Arias, Manuel Emilio Gegúndez ^a  

^a UNIVERSITY OF HUELVA   (Spain)

Author keywords

Fuzzy control; Lyapunov methods; Nonlinear systems; Stability

Indexed keywords

LYAPUNOV THEORIES; NON LINEAR CONTROL; NONLINEAR FUZZY CONTROL; SYNTHESIS PROCEDURE; SYSTEM DESIGN;

DIFFERENTIAL EQUATIONS; FUZZY CONTROL; FUZZY INFERENCE; FUZZY SYSTEMS; LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; NONLINEAR CONTROL SYSTEMS; SYSTEM STABILITY;

CONTROL SYSTEM STABILITY;

EID: 70350053410     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2009.2021984     Document Type: Article

References (42)

1. L. A. Zadeh, "Fuzzy sets," Inf. Control, vol. 8, no. 3, pp. 338-353, 1965.
2. J.M. Andújar, A. J. Barragán, M. E. Gegúndez, andM. Maestre, "Control borroso multivariable basado en heurística. un caso práctico: Grúa porta contenedores," Revista Iberoamericana Automát. Inf. Ind. (RIAI), vol. 4, no. 2, pp. 81-89, 2007.
3. ∞ fuzzy control design for nonlinear singularly perturbed systems with pole placement constraints: An LMI approach," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 1, pp. 579-588, Feb. 2004.
4. T. M. Guerra and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form," Automatica, vol. 40, no. 5, pp. 823-829, May 2004.
5. S. K. Hong and Y. Nam, "Stable fuzzy control system design with pole-placement constraint: An LMI approach," Comput. Ind., vol. 51, no. 1, pp. 1-11, May 2003.
6. H. Lam, F. Leung, and P. Tam, "An improved stability analysis and design of fuzzy control systems," in Proc. IEEE Int. Fuzzy Syst. Conf. (FUZZ-IEEE), Aug. 1999, vol. 1, pp. 430-433.
7. H. K. Lam, F. M. Leung, and P. K. S. Tam, "A linear matrix inequality approach for the control of uncertain fuzzy systems," IEEE Control Syst. Mag., vol. 22, no. 4, pp. 20-25, Aug. 2002.
8. K. Tanaka, T. Ikeda, and H. O. Wang, "Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 250-265, May 1998.
9. K. Tanaka, T. Hori, and H. Wang, "A fuzzy Lyapunov approach to fuzzy control system design," in Proc. Amer. Control Conf., Jun. 2001, vol. 6, pp. 4790-4795.
10. K. Tanaka, H. Ohtake, and H. O.Wang, "A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions," IEEE Trans. Fuzzy Syst., vol. 15, no. 3, pp. 333-341, Jun. 2007.
11. J. M. Andújar and J.M. Bravo, "Multivariable fuzzy control applied to the physical-chemical treatment facility of a cellulose factory," Fuzzy Sets Syst., vol. 150, no. 3, pp. 475-492, Mar. 2005.
12. J. M. Andújar, A. J. Barragán, J.M. Córdoba, and I. Fernández, "Diseño de sistemas de control borroso: Modelado de la planta," Revista Iberoamericana Automát. Inf. Ind. (RIAI), vol. 3, no. 1, pp. 75-81, Jan. 2006.
13. J. M. Andújar, J. Aroba, M. L. De la Torre, and J. A. Grande, "Contrast of evolution models for agricultural contaminants in ground waters by means of fuzzy logic and data mining," Environ. Geol., vol. 49, no. 3, pp. 458-466, 2006.
14. J. M. Andújar andA. J. Barragán, "Amethodology to design stable nonlinear fuzzy control systems," Fuzzy Sets Syst., vol. 154, no. 2, pp. 157-181, Sep. 2005.
15. J. M. Andújar, J. M. Bravo, and A. Peregrín, "Stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic," Fuzzy Sets Syst., vol. 148, no. 3, pp. 337-353, Dec. 2004.
16. A. Isidori, Nonlinear Control Systems II. London, U.K.: Springer-Verlag, 1999.
17. H. K. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice-Hall, 2000.
18. S. Sastry, Nonlinear System: Analysis, Stability, and Control. New York: Springer-Verlag, 1999.
19. J.-J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
20. H. J. Marquez, Nonlinear Control Systems. Analysis and Design. New York: Wiley, 2003.
21. L.-X. Wang, "Fuzzy systems are universal approximators," in Proc. IEEE Int. Conf. Fuzzy Syst., San Diego, CA, 1992, pp. 1163-1170.
22. B. Kosko, "Fuzzy systems as universal approximators," IEEE Trans. Comput., vol. 43, no. 11, pp. 1329-1333, Nov. 1994.
23. H. Ying, "Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 28, no. 4, pp. 515-520, Jul. 1998.
24. K. Zeng, N.-Y. Zhang, and W.-L. Xu, "A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 773-780, Dec. 2000.
25. R. Rovatti, "Fuzzy piecewise multilinear and piecewise linear systems as universal approximators in Sobolev norms," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 235-249, May 1998.
26. V. Kreinovich, H. T. Hguyen, and Y. Yam, "Fuzzy systems are universal approximators for a smooth function and its derivatives," Int. J. Intell. Syst., vol. 15, no. 6, pp. 565-574, Jun. 2000.
27. A. Mencattini, M. Salmeri, and A. Salsano, "Sufficient conditions to impose derivative constraints on MISO Takagi-Sugeno fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 13, no. 4, pp. 454-467, Aug. 2005.
28. V. Kreinovich, C. G. Mouzouris, and H. T. Hguyen, Fuzzy Rule Based Modeling as a Universal Approximation Too (Fuzzy Systems: Modeling and Control), H. T. Nguyen and M. Sugeno, Eds. Norwell, MA: Kluwer, 1998.
29. R. Babǔska, "Fuzzy modeling - A control engineering perspective," in Proc. FUZZ-IEEE/IFES, Yokohama, Japan, Mar. 1995, vol. 4, pp. 1897-1902.
30. R. Babǔska and H. B. Verbruggen, "A new identification method for linguistic fuzzy models," in Proc. FUZZ-IEEE/IFES, Yokohama, Japan, Mar. 1995, vol. 4, pp. 905-912.
31. T. Nguyen, M. Sugeno, R. Tong, and R. R. Yager, Theoretical Aspects of Fuzzy Control. New York: Wiley, 1995.
32. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no. 1, pp. 116-132, Feb. 1985.
33. L. Wong, F. Leung, and P. Tam, "Stability design of TS model based fuzzy systems," in Proc. IEEE Int. Conf. Fuzzy Syst., Barcelona, Spain, Jul. 1997, vol. 1, pp. 83-86.
34. T. Taniguchi, K. Tanaka, H. Ohtake, and H. O. Wang, "Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 9, no. 4, pp. 525-538, Aug. 2001.
35. M. Setnes, R. Babuŝka, U. Kaymak, and H. R. van Nauta Lemke, "Similarity measures in fuzzy rule base simplification," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 28, no. 3, pp. 376-386, Jun. 1998.
36. R. Babuŝka, M. Setnes, U. Kaymak, and H. R. van Nauta Lemke, "Rule base simplification with similarity measures," in Proc. 5th IEEE Int. Conf. Fuzzy Syst., vol. 3, New Orleans, LA, Sep. 1996, pp. 1642-1647.
37. Y. Yam, P. Baranyi, and C.-T. Yang, "Reduction of fuzzy rule base via singular value decomposition," IEEE Trans. Fuzzy Syst., vol. 7, no. 2, pp. 120-132, Apr. 1999.
38. M.-Y. Chen and D. A. Linkens, "Rule-base self-generation and simplification for data-driven fuzzy models," Fuzzy Sets Syst., vol. 142, no. 2, pp. 243-265, Mar. 2004.
39. W. H. Press, Numerical Recipes in C: The Art of Scientific Computing 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1998, ch. 2, pp. 96-97.
40. D. E. Goldberg, Genetic Algorithms in Search, Optimization & Machine Learning. Reading, MA: Addison-Wesley, 1989.
41. J. A. Nelder and R. A. Mead, "A simplex method for function minimization," Comput. J., vol. 7, no. 4, pp. 308-313, 1965.
42. T. A. Johansen, "Computation of Lyapunov functions for smooth nonlinear systems using convex optimization," Automatica, vol. 36, no. 11, pp. 1617-1626, Nov. 2000.