Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification |
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Authors: | Selami Beyhan Musa Alci |
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Affiliation: | 1. Industrial Engineering Department, Texas Tech University, Lubbock, TX, USA;2. School of Engineering and Sciences, Tecnológico de Monterrey, Monterrey, Nuevo León, México;1. School of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China;2. Hunan Engineering Laboratory for Advanced Control and Intelligent Automation, Changsha, Hunan 410083, China;3. Swan College, Central South University of Forestry and Technology, Changsha, Hunan 410201, China |
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Abstract: | In this study, auto regressive with exogenous input (ARX) modeling is improved with fuzzy functions concept (FF-ARX). Fuzzy function with least squares estimation (FF-LSE) method has been recently developed and widely used with a small improvement with respect to least squares estimation method (LSE). FF-LSE is structured with only inputs and their membership values. This proposed model aims to increase the capability of the FF-LSE by widening the regression matrix with lagged input–output values. In addition, by using same idea, we proposed also two new fuzzy basis function models. In the first, basis of the fuzzy system and lagged input–output values are structured together in the regression matrix and named as “L-FBF”. Secondly, instead of using basis function, the membership values of the lagged input–output values are used in the regression matrix by using Gaussian membership functions, called “M-FBF”. Therefore, the power of the fuzzy basis function is also enhanced. For the corresponding models, antecedent part parameters for the input vectors are determined with fuzzy c-means (FCM) clustering algorithm. The consequent parameters of the all models are estimated with the LSE. The proposed models are utilized and compared for the identification of nonlinear benchmark problems. |
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