Computing an appropriate control strategy based only on a given plant´s rule-based model is NP-hard

Traditional control starts with the description (i.e. model) of a plant, and an objective to be achieved. Based on this information, methods of traditional control theory enables one to compute a control strategy. In fuzzy control, one usually does not have an accurate model of the plant and one often can not express an objective in precise mathematical terms. Instead, one has a collection of "fuzzy" rules that an expert uses to control or describe the operation of a plant. Fuzzy control methodology enables the transformation of these "fuzzy" rules into a precise control strategy. For many interesting plants it has been possible to transform a "fuzzy" model into a control strategy. However, no efficient algorithm is known for the general case. In this paper, the authors show that the problem of transforming a rule-based model of a plant into an appropriate control strategy is in the general case NP-hard. This means that although in some cases, one does not need an expert controller, in some other cases one cannot control without his/her expertise