Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification

An adaptive extended fuzzy function state-observer based control with unknown control direction

“…Following that using gradient-descent and recursive-least-squares modeling with adaptive learning rates, one of the superior membership functions in [27] is designed for online system identification and high performance of the online function approximation was obtained for different benchmark systems [28]. In this study, we apply the following fuzzy function model for online system identification in indirect adaptive control of nonlinear systems with unknown control direction.…”

“…The above procedure is given for the offline FF-LSE modeling, then FF-LSE modeling was enhanced via augmenting the autoregressive with exogenous input model (ARX) and constructed different FF-ARX membership functions [27]. Following that using gradient-descent and recursive-least-squares modeling with adaptive learning rates, one of the superior membership functions in [27] is designed for online system identification and high performance of the online function approximation was obtained for different benchmark systems [28].…”

“…In addition, the fuzzy function model is extended using the type-2 fuzzy modeling concept [35]. Following to the above developments, fuzzy function-based auto regressive with exogenous-input (FF-ARX) regressor models that structures the input measurements as scalars and also other ARX terms located in regression matrix in [27]. Consequently, known ARX linear modeling and fuzzy system nonlinear modeling abilities are unified to get better identification performance.…”

“…Consequently, known ARX linear modeling and fuzzy system nonlinear modeling abilities are unified to get better identification performance. Finally, the a highly efficient FFARX model, which was introduced in study [27], is utilized for adaptive system identification and its convergence properties is detailed in [28].…”

Parallel Based Support Vector Regression for Empirical Modeling of Nonlinear Chemical Process Systems

“…Over the years, numerous nonlinear empirical models have been reported in literature, e.g. Volterra models (Ljung 2010;Mahmoodi 2007), artificial neural networks (Norgaard 2000), fuzzy-logic based models (Beyhan & Alci 2010), nonlinear auto regressive with exogenous input (NARX) models (Nelles 2001), some combinations of them like neuro-fuzzy models (Babuška & Verbruggen 2003), support vector machine and kernel methods of modeling (Tötterman & Toivonen 2009) and wavelet decomposition based methods (Billings 2005). One modeling technique that has been gaining popularity in the recent past is the support vector machine (SVM) (Suganyadevi & Babulal 2014;Tötterman & Toivonen 2009).…”