Design and analysis of a class of self-organizing and trainable fuzzy controllers

As the applications of fuzzy-controllers become more complicated, the attributes of self-organization and trainability become increasingly important. Indeed, the specification of fuzzy rules and membership functions for systems with a large number of state variables is extremely difficult. This paper introduces a new class of self-organizing and trainable fuzzy-controllers that can be designed without specific information regarding either the membership functions or the fuzzy rules. The proposed controller derives the fuzzy rules from clusters formed in the input space, through a self-organizing process. The clustering is performed through a simple method which can adaptively allocate new clusters as more date are available to the controller. Then, the membership values of crisp inputs are determined by K-nearest-neighbor (KNN) distance measures applied to the centers of the input clusters. Finally, a KNN defuzzification processes directly estimates of the crisp output of unknown input data. An adaptation procedure for the center vector of each cluster and the corresponding output value is developed. The overall design is analyzed in terms of the existence and the uniqueness of the solution of the proposed model. The performance of the proposed controller is considered through the modeling of the Mackey—Glass time-series.