Modelling of Nonlinear Systems Based on Fuzzy Clustering and Cubic Splines

This paper proposes a novel methodology for modelling nonlinear systems based on fuzzy clustering and cubic splines. The Gustafson-Kessel algorithm (G-K) is used in order to classify, in a database of input/output (I/O) measurements, the clusters with linear trends. Every three different and ordered consecutive clusters, contain a maximum and/or a minimum, which can be taken as the points of inflexion. Then, for every three clusters a cubic spline is figure out. Also, the intersection with the next cluster is smoothed with fuzzy submodels. An automation of the whole modelling process with a minimized number of rules with respect to linear submodels is then achieved, which is a clear improvement on the classical Takagi-Sugeno (T-S) models. By means of a simple example, the modelling algorithm is illustrated