Research On Nonlinear System Identification Using Fuzzy Clustering

In the field of control engineering, the nonlinear system's modeling and identification is an important part of control, management and fault diagnosis system design. Considering the defect of the traditional methods in modeling the complex and uncertain systems, a global function or an analytic structure that can describe the nonlinear systems becomes a necessity. Zadeh proposed an effective method to describe the complex or pathological systems which can not be expressed by a precise mathematical model. In recent years, the application of the fuzzy logic theory in the basic theory research of nonlinear system identification has made some progress and has formed a relatively complete theoretical framework.In the system modeling, there are many ways to apply the theory of fuzzy set and the concept of fuzzy logic, with the following one being the most widely used----the fuzzy rule based systems in which the relation between system variables is through if-then rules. As to this type of systems, most of the in-depth studies focus on the T-S fuzzy model. Thus, fuzzy clustering algorithm is applied for fuzzy partion of T-S fuzzy model in this article.The Fuzzy C-Mean (FCM) that is based on objective functions is a fuzzy clustering algorithm of great maturity. At first, the paper makes the space partition for the identification of the T-S Fuzzy Model by using the G-K and the FCM clustering algorithms. Then an improved fuzzy partion clustering algorithm is used to make up the defects of the FCM algorithm itself. At last, the simulation results show that this algorithm can improve the recognition accuracy to a certain extent.The Fuzzy C-Regression Model (FCRM) serves as a hyperplane classification of the input-output datum. It divides the datum into several classes, each of which is corresponding to a regression model. Therefore, the data spatial structure of the T-S Fuzzy Model is precisely described. Basing on the FCRM algorithm, an improved fuzzy partition method to the objective functions of FCM algorithm so as to improve the accuracy of identification is proposed in this article.In fuzzy systems that are based on fuzzy functions, the modeling methods use some fuzzy functions rather than the if-then rules to describe the system characteristics----a set of linear or nonlinear function in concrete. The input variables also include the current membership of input variable, or the conversion of some form of membership apart from the system input variables. The number of the fuzzy clustering in the input variables equals to the number of functions in the fuzzy function system. In this paper, the FCRM distance is added into the distance among the FCM samples in order to improve the identification accuracy of the system. The main work and innovations are as follows:1. By using G-K and the FCM clustering algorithms, two T-S fuzzy models has been described, identified and studied respectively.2. An improved fuzzy partion clustering is applied for T-S fuzzy model identification.3. Propoed an improved fuzzy c-regression model clustering algorithm for T-S fuzzy model identification.4. Propoed a fuzzy function system identification method based on hybrid clustering algorithm.