Fuzzy control as a universal control tool

Abstract It is known that fuzzy control is a universal control tool , because an arbitrary control strategy (in particular, a control strategy that is in some sense optimal) can be obtained in principle by applying a fuzzy control methodology to some set of rules. This result has already been proved (e.g., [2, 7, 20, 21]) for the case when a plant is described by finitely many parameters and a special type of fuzzy control methodology is used. In this paper, we prove it for arbitrary plants (including plants that are distributed systems , i.e., plants whose state requires infinitely many parameters to describe) and arbitrary fuzzy control methodologies. We also prove that there exists a universal fuzzy controller that generates an appropriate control from an input description of a plant (and the desired objective). Mathematically, we prove that fuzzy systems can approximate arbitrary continuous functionals, thus generalizing a known result about continuous functions.