Fuzzy control as a universal control tool

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 nitely 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 innnitely 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.