Compact TS - Fuzzy Models Through Clustering and OLS Plus FIS Model Reduction

The identification of uncertain and nonlinear systems is an important and challenging problem. Fuzzy logic models are often a good choice to describe such systems, however in many cases these become complex soon. Generally, too less effort is put into variable selection and in the creation of suitable local rules. Moreover, in general no model reduction is applied, while this may simplify the model by removing redundant information. This paper proposes a combined method that handles these issues in order to create compact Takagi-Sugeno (TS) models that can be effectively used to represent complex systems. A new fuzzy clustering method is proposed for the identification of compact TS-fuzzy models. The most relevant consequent variables of the TS model are selected by an orthogonal least squares method based on the obtained clusters. For the selection of the relevant antecedent (scheduling) variables a new method has been developed based on Fisher’s interclass separability criteria. This overall approach is demonstrated by means of the MPG (miles per gallon) nonlinear regression benchmark. The results are compared with results obtained by standard linear, neuro-fuzzy and advanced fuzzy clustering based identification tools.