From Fuzzy Models to Fuzzy Control

Traditional (non-fuzzy) control methodology deals with situations when we know exactly how the system behaves and how it will react to diierent controls, and we want to choose an appropriate control strategy. This methodology enables us to transform the description of the plant's (system's) behavior into an appropriate control strategy. In many practical situations, we do not have the exact knowledge of the system's behavior, but we have expert-supplied fuzzy rules which describe this behavior. In such situations, it is desirable to transform these description rules into rules describing control. There exist several reasonable heuristics for such transformation; however, the lack of formal justiica-tion restricts their applicability. In this paper, we provide a justiication for the most natural of the known heuristics: whenever we have a description rule \if A(x) and B(u) then C(_ x)", and we want to achieve _ x = d(x), add a control rule \if A(x) and C(d(x)), then B(u)".