Abstract

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 L2space 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.

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