Generalized Fuzzy Automata for Fuzzy Feedback Control with Words

Abstract

A model of fuzzy control based on Generalized Fuzzy Automata (GFA) is proposed. The fuzzy controllers based on the GFA theory control plants with words since system states, inputs, and outputs are encoded in linguistic terms when modeling with GFAs. Therefore, the behavior of a control system is described with words. Mathematically we prove that GFA realize general fuzzy feedback controls. This novelty provides implementation, no matter in hardware or software, of fuzzy feedback controllers in a systematic, unified, effective, and objective paradigm. The properties of the rule base including fuzzy rules and membership functions of the controller are objectively defined without much subjective domain expertise involved. The proofs also demonstrate how fuzzy feedback control with words is performed.