Continuity of Fuzzy Controller

Abstract - In this work, we study fuzzy control using the membership function of the“then” part of a fuzzy rule, which is in L 2 space. The compactness of a set ofmembership functions and the continuity of a fuzzy controller, the existence of fuzzyoptimal control is described. 1. Introduction Since Zadeh introduced the notion of fuzziness and fuzzy sets in 1965 ([1]), it hasbeen applied to various fields of engineering. The emphasis of these applications is in thefield of control, and recently various works in practical research have been conducted in thearea of fuzzy control. However, unlike the theory of classical control and modern control,systematized considerations have not been discussed sufficiently. The authors consider optimal control problems as the problem of finding the minimum(maximum) values of functions by treating control laws as problems of functionapproximation. The feedback laws of the control that are defined by nonlinear functionsare expressed as if-then type rules. The authors have discussed the compactness and theapplication of a membership function set