Polynomial fuzzy models for nonlinear control: A taylor series approach

IEEE Transactions on Fuzzy Systems

Volumn 17, Issue 6, 2009, Pages 1284-1295

  Sala, Antonio ^a   Ariño, Carlos ^b  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

^b UNIVERSITAT JAUME I   (Spain)

Author keywords

Fuzzy control; Fuzzy modeling; Polynomial fuzzy systems; Relaxed stability conditions; Sum of squares (SOS)

Indexed keywords

CONTROLLER SYNTHESIS; CONVEX COMBINATIONS; FIRST-PRINCIPLES; FUZZY MODELING; FUZZY MODELS; GENERALIZED POLYNOMIALS; LOCAL MODEL; MODELING TECHNIQUE; NON LINEAR CONTROL; NON-LINEARITY; POLYNOMIAL CASE; POLYNOMIAL MODELING; STABILITY ANALYSIS; STABILITY CONDITION; SUM OF SQUARES; T S MODELS; TAKAGI-SUGENO FUZZY MODELS;

CONTROL SYSTEM STABILITY; FUZZY SYSTEMS; MATHEMATICAL MODELS; MEMBERSHIP FUNCTIONS; NONLINEAR CONTROL SYSTEMS; NONLINEAR EQUATIONS; POLYNOMIALS; SYSTEM STABILITY;

FUZZY CONTROL;

EID: 72649103386     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2009.2029235     Document Type: Article

References (35)

1. A. Sala, T. M. Guerra, and R. Babuška, "Perspectives of fuzzy systems and control," Fuzzy Sets Syst., vol.156, no.3, pp. 432-444, 2005.
2. G. Feng, "A survey on analysis and design of model-based fuzzy control systems," IEEE Trans. Fuzzy Syst., vol.14, no.5, pp. 676-697, Oct. 2006.
3. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modelling and control," IEEE Trans. Syst., Man Cybern., vol.SMC-15, no.1, pp. 116-132, Feb. 1985.
4. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis. New York: Wiley, 2001.
5. S. Boyd, L. ElGhaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
6. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
7. S. Prajna, A. Papachristodoulou, P. Seiler, and P. A. Parrilo, SOSTOOLS: Sum of Squares Optimization Toolbox for MATLAB, California Inst. Technol., Pasadena, 2004.
8. A. Sala (2007). Reducing the gap between fuzzy and nonlinear control (invited talk). in Proc. 3rd IFAC Workshop Adv. Fuzzy-Neural Control, Valenciennes, France [Online]. pp. 1-6. Available: http://www.ifacpapersonline. net/
9. A. Sala, "On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems," Annu. Rev. Control, vol.33, pp. 48-58, 2009.
10. S. Prajna, A. Papachristodoulou, and F. Wu, "Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach," in Proc. 5th Asian Control Conf., 2004, vol.1, pp. 157-165.
11. A. Sala and C.V. Ariño, "Relaxed stability and performance LMI conditions for Takagi-Sugeno fuzzy systems with polynomial constraints on membership shape," IEEE Trans. Fuzzy Syst., vol.16, no.5, pp. 1328-1336, Oct. 2008.
12. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, "A sum of squares approach to stability analysis of polynomial fuzzy systems," in Proc. Amer. Control Conf., 2007, pp. 4071-4076.
13. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, "Stabilization of polynomial fuzzy systems via a sum of squares approach," in Proc. IEEE 22nd Int. Symp. Intell. Control, 2007, pp. 160-165.
14. K. Tanaka, H. Ohtake, and H. O. Wang, "Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol.39, no.2, pp. 561-567, Apr. 2009.
15. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, "A sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems" IEEE Trans. Fuzzy Syst., vol.17, no.4, pp. 911-922, Aug. 2009.
16. G. Blekherman, "There are significantly more nonegative polynomials than sums of squares," Israel J. Math., vol.153, no.1, pp. 355-380, 2006.
17. T. Bouarar, K. Guelton, and N. Manamanni, "LMI basedh? controller design for uncertain Takagi-Sugeno descriptors subject to external disturbances," presented at the IFAC Adv. Fuzzy-Neural Control, Valenciennes, France, 2007.
18. C. Ariño and A. Sala, "Relaxed LMI conditions for closed-loop fuzzy systems with tensor product structure," Eng. Appl. Artif. Intell., vol.20, pp. 1036-1046, 2007.
19. J. Abonyi, R. Babuska, and F. Szeifert, "Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol.32, no.5, pp. 612-621, Oct. 2002.
20. J. L. Diez, J. L. Navarro, and A. Sala, "A fuzzy clustering algorithm enhancing local model interpretability," Soft Comput., vol.11, pp. 973-983, 2007.
21. S. S. Ge, Stable Adaptive Neural Network Control. Norwell, MA: Kluwer, 2001.
22. S. Labiod and T. M. Guerra, "Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems," Fuzzy Sets Syst., vol.158, no.10, pp. 1126-1137, 2007. (Pubitemid 46428433)
23. P. Baranyi, "TP model transformation as a way to LMI-based controller design," IEEE Trans. Ind. Electron., vol.51, no.2, pp. 387-400, Apr. 2004.
24. L. Wu and D. Ho, "Fuzzy filter design for its stochastic systems with application to sensor fault detection," IEEE Trans. Fuzzy Syst., vol.17, no.1, pp. 233-242, Feb. 2009.
25. J. Bondia, A. Sala, J. Pićo, and M. A. Sainz, "Controller design under fuzzy pole-placement specifications: An interval arithmetic approach," IEEE Trans. Fuzzy Syst., vol.14, no.6, pp. 822-836, Dec. 2006.
26. D. Dubois and H. Prade, "Operations on fuzzy numbers," Int. J. Syst. Sci., vol.9, no.6, pp. 613-626, 1978.
27. A. Sala, J. L. Diez, J. L. Navarro, and P. Albertos, "Fuzzy model usage and readability in identification for control," in Proc. World Autom. Congr., 2004, vol.16, pp. 113-118.
28. H. J. Lee, J. B. Park, and G. Chen, "Robust fuzzy control of nonlinear systems with parametric uncertainties," IEEE Trans. Fuzzy Syst., vol.9, no.2, pp. 369-379, Apr. 2009.
29. A. Kruszewski, "Lois de commande pour une classe de mod̀eles non lińeaires sous la forme Takagi-Sugeno: Mise sous forme LMI," Ph.D. dissertation, Univ. Valenciennes et du Hainaut-Cambresis, Valenciennes, France, Dec. 2006.
30. A. Sala and C. Ariño, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem," Fuzzy Sets Syst., vol.158, no.4, pp. 2671-2686, 2007.
31. T. Apostol, Calculus, vol.1. New York: Wiley, 1967.
32. A. Kruszewski, A. Sala, T. M. Guerra, and C. V. Ariño, "A triangulation approach to asymptotically exact conditions for fuzzy summations," IEEE Trans. Fuzzy Syst., to be published. DOI: 10.1109/TFUZZ. 2009.2019124.
33. A. Sala and C. Ariño, "Relaxed stability and performance conditions for Takagi-Sugeno fuzzy systems with knowledge on membership function overlap," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol.37, no.3, pp. 727-732, Jun. 2007.
34. M. Bernal, T. M. Guerra, and A. Kruszewski, "A membership- functiondependentH ? controller design for Takagi-Sugeno models," in Proc. IEEE Int. Conf. Fuzzy Syst., 2008, pp. 1139-1145. DOI: 10.1109/FUZZY. 2008.4630514.
35. A. Sala, "Introducing shape-dependent relaxed conditions in fuzzy control of nonlinear systems in Tagaki-Sugeno form" in Proc. Fuzz Syst. IEEE (IEEE World Congress on Computational Intelligence) Int. Conf., Piscataway, NJ, Jun. 2008, pp. 512-517. DOI: 10.1109/FUZZY.2008.4630416.