Takagi-Sugeno Fuzzy Modeling and Control of Nonlinear System with Adaptive Clustering Algorithms

Abstract

In order to control a nonlinear system, a model needs to be established to predict its behavior. At present, there are many methods for nonlinear system modeling. Among them T-S fuzzy prediction model has attracted extensive attention due to its better generalization and excellent approximation in the dense region. Clustering algorithms can be used for the premise identification of the T-S model. But the optimal premise is not easy to be determined because of the difficulty to obtain optimal clustering number. For solving the shortcoming, a clustering validity function is described, based on which the clustering performance of adaptive fuzzy C-means clustering algorithm (adaptive FCM) is compared to that of the adaptive alternative fuzzy C-mean clustering algorithm (adaptive AFCM) with three datasets. Furthermore, two modeling algorithms for T-S fuzzy model using the adaptive FCM and the adaptive AFCM are designed, combining with the RLS, named adaptive FCM-RLS and adaptive AFCM-RLS. Finally, in order to demonstrate the effectiveness of the modeling methods in this paper, the T-S fuzzy model of a batch progress is constructed by adaptive FCM-RLS. With the T-S model, fuzzy generalized predictive controller is designed. Simulation results show that fuzzy-GPC controller has the better performances than GPC controller desisned with least square method.