Identification of uncertain nonlinear systems for robust fuzzy control

In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi–Sugeno (T–S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe t...

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Published in:	ISA transactions Vol. 49; no. 1; pp. 27 - 38
Main Authors:	Senthilkumar, D., Mahanta, Chitralekha
Format:	Journal Article
Language:	English
Published:	Kidlington Elsevier Ltd 2010 Elsevier
Subjects:	Algorithms Applied sciences Artificial Intelligence Computer science; control theory; systems Control system analysis Control system synthesis Control theory. Systems Data Interpretation, Statistical Electronics Exact sciences and technology Fuzzy Logic Interval fuzzy model Linear programming Modelling and identification Nonlinear Dynamics Parametric uncertainties Takagi–Sugeno (T–S) fuzzy model Uncertainty Linear programming Takagi–Sugeno (T–S) fuzzy model Interval fuzzy model Parametric uncertainties Robust stability Non linear control Control synthesis Non linear system Modeling Robust control Fuzzy logic Fuzzy control Time varying system Uncertain system Robustness System identification Time constant Takagi-Sugeno (T-S) fuzzy model
ISSN:	0019-0578, 1879-2022, 1879-2022
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Abstract	In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi–Sugeno (T–S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by S˘krjanc et al. (2005) [11,12]. With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.
AbstractList	In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by Skrjanc et al. (2005). With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control. In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi–Sugeno (T–S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by S˘krjanc et al. (2005) [11,12]. With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control. In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by Skrjanc et al. (2005). With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by Skrjanc et al. (2005). With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.
Author	Senthilkumar, D. Mahanta, Chitralekha
Author_xml	– sequence: 1 givenname: D. surname: Senthilkumar fullname: Senthilkumar, D. email: d.senthil@iitg.ernet.in, senthildsenthil@gmail.com – sequence: 2 givenname: Chitralekha surname: Mahanta fullname: Mahanta, Chitralekha email: chitra@iitg.ernet.in
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Keywords	Linear programming Takagi–Sugeno (T–S) fuzzy model Interval fuzzy model Parametric uncertainties Robust stability Non linear control Control synthesis Non linear system Modeling Robust control Fuzzy logic Fuzzy control Time varying system Uncertain system Robustness System identification Time constant Takagi-Sugeno (T-S) fuzzy model
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Snippet	In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi–Sugeno (T–S) form for the purpose of robust fuzzy control design. The... In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The...
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SubjectTerms	Algorithms Applied sciences Artificial Intelligence Computer science; control theory; systems Control system analysis Control system synthesis Control theory. Systems Data Interpretation, Statistical Electronics Exact sciences and technology Fuzzy Logic Interval fuzzy model Linear programming Modelling and identification Nonlinear Dynamics Parametric uncertainties Takagi–Sugeno (T–S) fuzzy model Uncertainty
Title	Identification of uncertain nonlinear systems for robust fuzzy control
URI	https://dx.doi.org/10.1016/j.isatra.2009.07.005 https://www.ncbi.nlm.nih.gov/pubmed/19683234 https://www.proquest.com/docview/733863613
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