A fuzzy system can be constructed to interpolate between input-output data to provide an approximation for the function that is implicitly defined by the input-output data pair associations. In this paper the authors begin by explaining how function approximation techniques can be used to solve nonlinear estimation and system identification problems. Next, the authors discuss several fundamental issues related to how to choose the input-output data pairs so that accurate function approximation can be achieved with fuzzy systems. The authors' main result is a new technique for function approximation via fuzzy systems where they specify membership functions and add rules to try to achieve a pre-specified function approximation accuracy. The authors illustrate the new technique on an actuator failure detection and identification problem for the F-16 aircraft.
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