A self‐organizing knn fuzzy controller and its neural network structure

This paper introduces a fuzzy controller that can be designed without specific information on the membership functions and the fuzzy rules. We show how the membership values of crisp inputs can be determined by K‐nearest‐neighbour (KNN) distance measures applied to the centres of the input clusters. Based on this new type of membership values, we introduce a KNN defuzzification method that allows the direct estimation of the crisp output of the given input data. the proposed computational model requires a clustering (self‐organizing) process. We employ a simple clustering method that can adaptively allocate new clusters as more data become available to the controller. We prove that the resulting controller can uniformly approximate any real and continuous function to any desirable accuracy on a compact set. For hardware implementations we develop a neural network structure of the proposed fuzzy controller and compare it with other types of neural networks. It is shown that the three‐layer sigmoid neural network and the Gaussian radial basis function (GRBF) network are special cases of this structure. A learning algorithm for the new structure is provided. the performance of the proposed controller is considered through three application studies: a controller design for truck backer‐upper control, the prediction of the S&P 500 index, and the prediction of the Mackey‐Glass time series.