Abstract
The purpose of this study is to consider the fuzzy optimal control based on the functional analysis. We used a mathematical approach to compute optimal solutions. The feedback of fuzzy control is evaluated through approximate reasoning using the center of sums defuzzification method or the height method on IF-THEN fuzzy rules. 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 continuous function space is compact metrizable. 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 minimizes (maximizes) the integral performance function of the nonlinear feedback fuzzy system.
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