FUZZY CONTROLLER CAN BE LIPSCHITZ CONTINUOUS

BÁRTOVÁ, D.; KUKAL, J.; MAJEROVÁ, D.

Abstract

Any traditional fuzzy controller performs a sequence of three processes: fuzzyfication, control algorithm and defuzyfication. It is useful when the controller exhibits continuous behavior with constrained output and sensitivity. After the normalization of controller inputs and outputs into interval [0;1] we designed the fuzzy controller to be Lipschitz continuous, which implies the constrained sensitivity of the controller. Lukasiewicz algebra enriched by square root function (LAsqrt) was used for the realization of proposed fuzzy controller. The realization of fuzzification and control algorithm is trivial. The only one problem is in the defuzzyfication. Neither Mamdani nor Larsen approaches are continuous in general. Both MOM and COG techniques generate discontinuous output behavior. That is why we developed a new defuzzification method based on Lukasiewicz algebra. Thus, proposed technique of defuzzyfication 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.

Coresponding author e-mail: Darina[dot]Bartova[at]vscht[dot]cz

Session: Intelligent Control Systems