A novel cost function based on decomposing least‐square support vector machine for Takagi–Sugeno fuzzy system identification

Abstract

This study develops and illustrates a novel cost function which is the combination of these terms constituted of decomposing least square-support vector machine (LS-SVM) and error terms for the identification of Takagi-Sugeno (T-S) fuzzy system based only on measured data without any prior knowledge. The proposed method combines the advantages of fuzzy system theory and some ideas from LS-SVM. Firstly, Gustafson-Kessel clustering algorithm is applied to split training data into R clustering subsets. Likewise, LS-SVM is also decomposed into R terms and consequent parameters a k for T-S fuzzy system corresponding to these terms obtained by decomposing LS-SVM are combined with the error terms to form the new total cost function. Following that, this constrained optimisation problem based on the total cost function can be solved by applying the Lagrange technique. The resulting fuzzy system generated by this method has the following distinct features: (i) the obtained new cost function can be regarded as a structural risk instead of empirical risk; (ii) although incorporating LS-SVM concept into the cost function of T-S fuzzy model, it is shown that the computation process cannot only avoid the selection of kernel function, but also merely use the scalar product for original input space to further reduce the calculation greatly; and (iii) as seen in the proposed novel cost function, the approach can well guarantee the performance of both local-regression models and global model. Finally, the viability and superiority of the method are verified by simulation.