Validation of the control quality of characteristic field based fuzzy controllers

Rule based systems for Fuzzy Control, Fuzzy Supervising and Fuzzy Diagnosis are non-linear multi-input, multi-output systems. The result of the signal processing within the system is a high dimensional characteristic field. For optimizing the behaviour of the system, we have a high number of fiee degrees. The reconstruction of the knowledge base from the characteristic field as starting point is impossible. With this background, the paper describes the quality of a two dimensional Fuzzy Controller characteristic field in connection with the necessary deformation for the compensation of non-linear effects. We will demonstrate that one should define two restrictions for the characteristic field: continuity without local extrema and differentiability. Under such conditions we need only two fiee degrees for optimizing the controller behaviour using the characteristic field deformation. A related example will be presented.