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 fuz
zy control methodology to some set of rules. This result has already b
een proved (e.g., [2, 7, 20, 21]) for the case when a plant is describ
ed by finitely many parameters and a special type of fuzzy control met
hodology is used. In this paper, we prove it for arbitrary plants (inc
luding plants that are distributed systems, i.e., plants whose state r
equires infinitely many parameters to describe) and arbitrary fuzzy co
ntrol methodologies. We also prove that there exists a universal fuzzy
controller that generates an appropriate control from an input descri
ption 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.