Continuity of Nakamori fuzzy model and its application to optimal feedback control

This paper describes optimization of nonlinear feedback fuzzy system using Nakamori ´s approximate reasoning. The fuzzy control discussed here is the nonlinear feedback control in which the feedback laws are determined by IF-THEN type fuzzy production rules through Nakamori´s approximate reasoning. To prove existence of optimal control, we applied compactness of a set of membership functions in L^∞ space and continuity of the approximate reasoning, and prepared some propositions concerning the Nakamori ´s approximate reasoning. By considering fuzzy optimal control problems as problems of finding the minimum (maximum) value of the integral cost (benefit) function on an appropriate set of membership functions, the existence of fuzzy optimal control is shown.