Designing fuzzy controllers by rapid learning

We propose a learning approach to designing fuzzy controllers based on the B-spline model. Unlike other normalised parameterised set functions for defining fuzzy sets, B-spline basis functions do not necessarily span from membership values zero to one, but possess the property "partition of unity". B-spline basis functions can be automatically determined after each input is partitioned. Learning of a fuzzy controller based on B-spline basis functions is then equivalent to the adaptation of a B-spline interpolator. Parameters of the controller output of each rule can be adapted by using the gradient descent method. Optimal placements of the B-spline basis functions for specifying each input can be found by an algorithm working similarly to a self-organising neural network. Through comparative examples of function approximation we show that learning of such a fuzzy controller generally converges fast. This approach can be extended to the problems of supervised as well as unsupervised learning.