A comparison between fuzzy, PI and B-spline control

The authors compare fuzzy control with classical interpolation techniques like B-splines. A B-spline controller 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, much smoother control surfaces can be obtained than with the usual fuzzy operators, and a linear proportional-integral (PI) controller can also be obtained readily. This viewpoint suggests new ways to adapt fuzzy controllers. A comparison with neural networks is made