This article presents a mathematical framework for studying the existence of optimal feedback control based on IF-THEN fuzzy
rules through approximate reasoning, and introduces the notion of an admissible fuzzy controller. The framework consists of
two propositions: To guarantee the convergence of optimal solution, a set of fuzzy membership functions (admissible fuzzy
controller) which are selected out of L
2 space is convex and compact metrizable for the weak topology. And assuming approximate reasoning to be a functional on the
set of membership functions, its continuity is proved. Then, we show the existence of a fuzzy controller which minimize (maximize)
the integral performance function of the nonlinear feedback system.
Keywords Fuzzy control - Functional analysis - Feedback systems - Optimization
The paper was supported in part by Grant-in-Aid for Young Scientists (B) #19700225 from Japan Society for the Promotion of
Science (JSPS).