ファジィ集合族のコンパクト性とファジィ最適制御の存在

抄録

This article presents a framework for studying the existence of optimal control based on fuzzy rules. The framework consists of two propositions : (1)The family of fuzzy membership functions with bounded gradients is a uniformly bounded, equicontinuous closed set. Hence the family of fuzzy membership functions is compact by Ascoli-Arzela's theorem.(2)The defuzzification function is continuous on the family of fuzzy membership functions with bounded gradients. Then the existence of fuzzy optimal control is proved.