Evolving Takagi-Sugeno model based on online Gustafson-Kessel algorithm and kernel recursive least square method

In this paper, we introduce an evolving Takagi-Sugeno model which utilizes an online Gustafson-Kessel algorithm for structure identification and sparse weighted kernel least square as local models. Our online clustering algorithm can form elliptical clusters which leads to creating less but more complex clusters than spherical ones. The proposed clustering method is capable of determining number of required clusters and reducing the complexity of model by merging similar clusters. Moreover, we propose weighted kernel recursive least square method with a new sparsification procedure based on instant prediction error. This sparsification procedure enhances kernel recursive least square performance. To illustrate our methodology, we apply the introduced algorithm to online identification of nonlinear and time varying system. Finally, to show the superiority of our approach in comparison to some known online approaches two different case studies are considered: Mackey-Glass and electrical load time series.