The Performance of B-Spline and Gaussian Functions in the Structure of a Neuro-Fuzzy Network

A fuzzy logic system has been shown capable of arbitrarily approximating any nonlinear function and has been successfully applied to system modeling. The functional rule fuzzy system enables the input-output relation of the fuzzy logic system to be analyzed. B-Spline basis functions have many desirable numerical properties and as such can be used as membership functions of fuzzy systems. Existing methods in implementing Neuro-Fuzzy controller usually insert B-Spline functions in their structures to execute fuzzy inference. Having recursive structure creates delay in B-Spline based Neuro-Fuzzy system and consequently makes extreme delay in control loops. In the current study, instead of the third order B-Spline function, a Gaussian function has been used which satisfies the conditions early in the B-Spline based Neuro-Fuzzy controller and also decreases time delay in the control loop and omits the effects of the system noises and uncertainties while working as an optimal filtering system. Since the processing speed in control systems is an important factor, the importance of this method will be shown.

Keywords:

Artificial Neural Network , Fuzzy Logic , Neuro-Fuzzy Controller , Gaussian and B-Spline Functions