Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching

Hak-Keung Lam; Hongyi Li; Christian Deters; E. L. Secco; Helge Wurdemann; Kaspar Althoefer

doi:10.1109/TIE.2013.2253064

Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching

Hak-Keung Lam, Hongyi Li, Christian Deters, E. L. Secco, Helge Wurdemann, Kaspar Althoefer

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Abstract

This paper focuses on designing interval type-2 (IT2) control for nonlinear systems subject to parameter uncertainties. To facilitate the stability analysis and control synthesis, an IT2 Takagi-Sugeno (T-S) fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are captured by IT2 membership functions characterized by the lower and upper membership functions. A novel IT2 fuzzy controller is proposed to perform the control process, where the membership functions and number of rules can be freely chosen and different from those of the IT2 T-S fuzzy model. Consequently, the IT2 fuzzy-model-based (FMB) control system is with imperfectly matched membership functions, which hinders the stability analysis. To relax the stability analysis for this class of IT2 FMB control systems, the information of footprint of uncertainties and the lower and upper membership functions are taken into account for the stability analysis. Based on the Lyapunov stability theory, some stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and achieve the control design. Finally, simulation and experimental examples are provided to demonstrate the effectiveness and the merit of the proposed approach.

Original language	English
Pages (from-to)	956-968
Number of pages	13
Journal	IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
Volume	61
Issue number	2
Early online date	20 Mar 2013
DOIs	https://doi.org/10.1109/TIE.2013.2253064
Publication status	Published - Feb 2014

Keywords

Fuzzy control, imperfect premise matching, interval type-2 (IT2) fuzzy control, stability analysis

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10.1109/TIE.2013.2253064

Control Design for Interval Type-2_LAM_Published Online 20 March 2013_GREEN AAM
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Cite this

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title = "Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching",

abstract = "This paper focuses on designing interval type-2 (IT2) control for nonlinear systems subject to parameter uncertainties. To facilitate the stability analysis and control synthesis, an IT2 Takagi-Sugeno (T-S) fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are captured by IT2 membership functions characterized by the lower and upper membership functions. A novel IT2 fuzzy controller is proposed to perform the control process, where the membership functions and number of rules can be freely chosen and different from those of the IT2 T-S fuzzy model. Consequently, the IT2 fuzzy-model-based (FMB) control system is with imperfectly matched membership functions, which hinders the stability analysis. To relax the stability analysis for this class of IT2 FMB control systems, the information of footprint of uncertainties and the lower and upper membership functions are taken into account for the stability analysis. Based on the Lyapunov stability theory, some stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and achieve the control design. Finally, simulation and experimental examples are provided to demonstrate the effectiveness and the merit of the proposed approach.",

keywords = "Fuzzy control, imperfect premise matching, interval type-2 (IT2) fuzzy control, stability analysis",

author = "Hak-Keung Lam and Hongyi Li and Christian Deters and Secco, {E. L.} and Helge Wurdemann and Kaspar Althoefer",

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doi = "10.1109/TIE.2013.2253064",

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AU - Deters, Christian

AU - Secco, E. L.

AU - Wurdemann, Helge

AU - Althoefer, Kaspar

PY - 2014/2

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N2 - This paper focuses on designing interval type-2 (IT2) control for nonlinear systems subject to parameter uncertainties. To facilitate the stability analysis and control synthesis, an IT2 Takagi-Sugeno (T-S) fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are captured by IT2 membership functions characterized by the lower and upper membership functions. A novel IT2 fuzzy controller is proposed to perform the control process, where the membership functions and number of rules can be freely chosen and different from those of the IT2 T-S fuzzy model. Consequently, the IT2 fuzzy-model-based (FMB) control system is with imperfectly matched membership functions, which hinders the stability analysis. To relax the stability analysis for this class of IT2 FMB control systems, the information of footprint of uncertainties and the lower and upper membership functions are taken into account for the stability analysis. Based on the Lyapunov stability theory, some stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and achieve the control design. Finally, simulation and experimental examples are provided to demonstrate the effectiveness and the merit of the proposed approach.

AB - This paper focuses on designing interval type-2 (IT2) control for nonlinear systems subject to parameter uncertainties. To facilitate the stability analysis and control synthesis, an IT2 Takagi-Sugeno (T-S) fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are captured by IT2 membership functions characterized by the lower and upper membership functions. A novel IT2 fuzzy controller is proposed to perform the control process, where the membership functions and number of rules can be freely chosen and different from those of the IT2 T-S fuzzy model. Consequently, the IT2 fuzzy-model-based (FMB) control system is with imperfectly matched membership functions, which hinders the stability analysis. To relax the stability analysis for this class of IT2 FMB control systems, the information of footprint of uncertainties and the lower and upper membership functions are taken into account for the stability analysis. Based on the Lyapunov stability theory, some stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and achieve the control design. Finally, simulation and experimental examples are provided to demonstrate the effectiveness and the merit of the proposed approach.

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Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching

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