Lipschitz continuity of fuzzy controller

• Autorzy: Bartova D. , Kukal J. , Majerova D.
• Języki publikacji: EN

Abstrakty

EN

Any traditional fuzzy controller performs a sequence of three processes: fuzzification, control algorithm and defuzzification. It is useful when the contoller exhibits continuous behavior with constrained output and sensitivity. After the normalization of controller inputs and outputs into the interval [0;1], we designed the fuzzy controller to be Lipschitz continuous, which implies the constrained sensitivity of the controller. Łukasiewicz algebra enriched by ŁAsqrt was used for the realization of the proposed fuzzy controller. The realization of fuzzification and control algotithm is trivial. The only problem is in the defuzzification. Neither Mamdani nor Larsen approaches are continuous in general. Both MOM and COG technoques generate discontinuous output behaviour. That is why we developed a new defuzzification method based on Łukasiewicz algebra. Thus, the proposed technique of defuzzification is based on propositional logic and it helps to realize a class of Lipschitz continuous fuzzy controllers. the controllers were realized in the Matlab environment.

Słowa kluczowe

EN

Łukasiewicz algebras; square root; Lipschitz coninuity; MATLAB; fuzzy control

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2006
• Tom: Vol. 16, no. 1
• Strony: 19--35
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Bartova D.

autor

Kukal J.

autor

Majerova D.

• ICT Praque, Department of Computing and Control Engineering, Technicka 5, 166 28 Praque 6 Dejvice Czech Republic,

Bibliografia

• [1] D. DRIANKOV, H. HELLENDOORN and M. REINFRANK: An Introduction to Fuzzy Control. Springer-Verlag, New York, 1993.
• [2] F. ESTEVA and L. GODO: Putting together Lukasiewicz and produkt logic. Mathware and soft computing, 6 (1999), 219-234.
• [3] V. NOVAK, I. PERFILIEVA and J. MOCKOR: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Boston, 1999.
• [4] R. R. YAGER and L. A. ZADEH: Mathematical principles of fuzzy logic. Kluwer Academic Publishers, 1991.
• [5] P. VYSOKY: Fuzzy rizeni. Skriptum CVUT, Praha, 1996, (in Czech).
• [6] D. MAJEROVA and J. KUKAL: Algebra a praxe: cesta k Lukasiewiczove algebre. Automatizace, 45 (2002), 562-566, (in Czech).
• [7] D. MAJEROVA and J. KUKAL: Modularni site v LA sqn. Automatizace, 46 2003, 302-304, (in Czech).