Fitting the Nonlinear Systems Based on the Kernel Functions Through Recursive Search

Membership function identification is an important part of studying fuzzy control theory. Gaussian membership functions are widely used in the defuzzification processes, while the simple fuzzy processing reduces the dynamic characteristics of models. In order to reflect the dynamic performance of th...

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Bibliographic Details
Published inInternational journal of control, automation, and systems Vol. 20; no. 6; pp. 1849 - 1860
Main Authors Li, Jimei, Rong, Yingjiao, Wang, Cheng, Ding, Feng, Li, Xiangli
Format Journal Article
LanguageEnglish
Published Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.06.2022
Springer Nature B.V
제어·로봇·시스템학회
Subjects
Algorithms
Control
Control theory
Dynamic characteristics
Engineering
Fuzzy control
Kernel functions
Mathematical models
Mechatronics
Nonlinear systems
Parameter estimation
Recursive functions
Regular Papers
Robotics
System effectiveness
제어계측공학
Gradient search
parameter estimation
multi-model control
nonlinear system
membership function
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Summary:Membership function identification is an important part of studying fuzzy control theory. Gaussian membership functions are widely used in the defuzzification processes, while the simple fuzzy processing reduces the dynamic characteristics of models. In order to reflect the dynamic performance of the nonlinear systems accurately, this paper introduces the idea of the multi-model control and fits a kernel function for the defuzzification processes by selecting the scheduling modes. Based on the gradient search, we present a least mean square (LMS) algorithm to solve the parameter estimation problem of the nonlinear systems. Considering the difficulty of determining the step sizes in the LMS algorithm, an overall stochastic gradient (O-SG) algorithm is deduced to obtain the optimal step size and estimate the unknown parameters. In order to improve the estimation accuracy, we introduce a forgetting factor into the O-SG algorithm to obtain the overall forgetting factor stochastic gradient (O-FFSG) algorithm. With the appropriate forgetting factors, the O-FFSG algorithm can effectively used for identifying the nonlinear systems. The performances of the proposed algorithms are tested by a numerical example.
Bibliography:http://link.springer.com/article/10.1007/s12555-020-0561-z
ISSN:1598-6446
2005-4092
DOI:10.1007/s12555-020-0561-z