TRAINING FUZZY-SYSTEMS TO PERFORM ESTIMATION AND IDENTIFICATION

A fuzzy system can be constructed to interpolate between input-output data to provide an approximation for the function that is implicitly d efined by the input-output data-pair associations. This paper begins b y explaining how function approximation techniques can be used to solv e nonlinear estimation and system identification problems. Next, sever al fundamental issues ave discussed, related to how to choose the inpu t-output data pairs so that accurate function approximation. can be ac hieved with fuzzy systems. Using this insight a technique called ''uni form training'' is proposed, in which input sequences are chosen to pr oduce good training data sets (''uniform training data sets''). Also, a new technique for function approximation via fuzzy systems called '' modified learning from examples'' is outlined, where membership functi ons are specified and rules ave added to try to achieve a pre-specifie d function approximation accuracy. Uniform training and the modified l earning from examples technique are then illustrated on a simple pendu lum example. In addition, the use of the modified learning from exampl es approach is demonstrated in constructing a fuzzy system which can i dentify actuator failures on an F-16 aircraft.