Fuzzy Controllers Design Using Space-Filling Curves

Abstract

In this paper we present a clustering technique for fuzzy rules based on Hilbert Space-filling Curves (SFC). SFC scans an n-dimensional space and reduces it to a curve, i.e. a one-dimensional line. The paper introduces first the Hilber Space-filling curves, and outlines algorithms for clustering and adaptive clustering which demonstrate the SFC efficient self-organizing features. We then propose a SFC fuzzy inference model based on clustering the object space. The SFC fuzzy model is then used to design a fuzzy controller. The proposed method achieves a dramatic reduction of the complexity of fuzzy controller by reducing the multivariable fuzzification problem to a one dimentional space.