Incremental TSK fuzzy modeling using hyperplane-based clustering

Abstract

Due to the linguistic presentation and the robust behavior, fuzzy modeling is widely used in many theoretical and industrial applications. Particularly, Takagi-Sugeno-Kang (TSK) fuzzy model has more attractive property to model an unknown complex nonlinear system accurately. In TSK fuzzy model, the complex function can be seen as local linear models. In data driven design of fuzzy model, clustering algorithms are usually employed to discover the model structure. However, most of clustering methods are used in offline manner. To fully utilize the concept of fuzzy system, the interpretable rule generation is important issue. The total system can be divided to linear submodels which describes their local behaviors. In this thesis, a new incremental hyperplane-based fuzzy clustering method to design a TSK fuzzy model is proposed. Starting from no rule, it generates clusters based on input similarity and distance from the consequent hyperplane incrementally. Membership functions are defined with statistical means and deviations of partitioned data. With this configuration, the obtained clusters reflect the real distribution of the training data points properly. The training equations are changed to recursive forms in order to applied in incremental framework. Some heuristic techniques to guarantee the initial training of each local submodel is used. In order to reduce the dependency on the order of training data, consecutive merge step is performed. Merge step is not only important for keeping rule bases compact and interpretable, but also provides the robustness to noise. Some simulations are carried out to show the advantages and performance of the proposed method. The proposed method is combined with multiple model approaches to control robot manipulators with varying payloads. The multiple fuzzy neural networks (FNNs) are used to approximate the changing system dynamics for various tasks. The multiple FNNs are generated dynamically by using incremental hyp...