Constancis, P. and Harris, C.J.
A Comparison between Fuzzy, PI and B-spline Control.
Int. Symp. on Intelligent Control
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Fuzzy control is a rule-based control in which fuzzy logic interpolates between production rules. That is why it interesting to compare it with classical interpolation techniques like B-splines. A B-spline function is a piecewise polynomial function. A B-spline controller is defined as a controller that maps inputs to outputs using a B-spline surface. This controller can be interpreted as a fuzzy controller with the probability operators product and sum instead of Zadeh operators min and max. B-splines also provide a framework for choosing the shape of the fuzzy sets. Using this method, we obtain much smoother control surfaces than with the usual fuzzy operators and can readily obtain a linear PI controller. This new viewpoint, which is very fruitful, suggests also new ways to adapt fuzzy controllers. A comparison with neural networks is made.
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