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Journals & Magazines >IEEE Transactions on Fuzzy Sy... >Volume: 27 Issue: 7

A New Design of Membership-Function-Dependent Controller for T-S Fuzzy Systems Under Imperfect Premise Matching

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Changzhu Zhang; Hak-Keung Lam; Jianbin Qiu; Chengju Liu; Qijun Chen
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Abstract:

This paper examines the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premis...Show More

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Abstract:

This paper examines the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premise variable space, the original T-S fuzzy model is equivalently converted into a piecewise-fuzzy system. Then, by employing some staircase functions, the continuous membership functions are approximated by a series of discrete values via which the information of membership functions is brought into the stability analysis to reduce the design conservatism. With piecewise-Lyapunov functions, the approaches to the piecewise-fuzzy state feedback and observer-based output feedback controller design are proposed, respectively, in terms of linear matrix inequalities such that the closed-loop system is asymptotically stable with a prescribed H∞ performance level. It is shown that the membership functions of the fuzzy model and fuzzy controllers are not necessarily the same, which allows more design flexibility. Finally, two illustrative examples are provided to show the effectiveness of the developed methods.
Published in: IEEE Transactions on Fuzzy Systems ( Volume: 27, Issue: 7, July 2019)
Page(s): 1428 - 1440
Date of Publication: 09 November 2018

ISSN Information:

DOI: 10.1109/TFUZZ.2018.2880424

Funding Agency:

Author image of Changzhu Zhang
Department of Control Science and Engineering, Tongji University, Shanghai, China
Changzhu Zhang  (M’11) received the B.S. degree in automation from Qufu Normal University, Rizhao, China, in 2007, the M.S. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2009, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2012.
From March 2013 to February 2014, he was an Associate Research Fellow with the...Show More
Changzhu Zhang  (M’11) received the B.S. degree in automation from Qufu Normal University, Rizhao, China, in 2007, the M.S. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2009, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2012.
From March 2013 to February 2014, he was an Associate Research Fellow with the...View more
Author image of Hak-Keung Lam
Department of Informatics, King's College London, London, U.K.
Hak-Keung Lam  (M’98–SM’10) received the B.Eng. (Hons.) and Ph.D. degrees from the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, in 1995 and 2000, respectively.
From 2000 to 2005, he was with the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, as a Postdoctoral Fellow and a Research Fellow. He joined King's College London, ...Show More
Hak-Keung Lam  (M’98–SM’10) received the B.Eng. (Hons.) and Ph.D. degrees from the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, in 1995 and 2000, respectively.
From 2000 to 2005, he was with the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, as a Postdoctoral Fellow and a Research Fellow. He joined King's College London, ...View more
Author image of Jianbin Qiu
State Key Laboratory of Robotics and Systems, and the Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, China
Jianbin Qiu  (M’10–SM’15) received the B.Eng. and Ph.D. degrees in mechanical and electrical engineering from the University of Science and Technology of China, Hefei, China, in 2004 and 2009, respectively, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Hong Kong, in 2009.
He is currently a Full Professor with the School of Astronautics, Harbin Institute of Technology, Harbin, China...Show More
Jianbin Qiu  (M’10–SM’15) received the B.Eng. and Ph.D. degrees in mechanical and electrical engineering from the University of Science and Technology of China, Hefei, China, in 2004 and 2009, respectively, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Hong Kong, in 2009.
He is currently a Full Professor with the School of Astronautics, Harbin Institute of Technology, Harbin, China...View more
Author image of Chengju Liu
Department of Control Science and Engineering, Tongji University, Shanghai, China
Chengju Liu received the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 2011.
From October 2011 to July 2012, she was a Research Associate with the BEACON Center, Michigan State University, East Lansing, MI, USA. From March 2011 to June 2013, she was a Postdoctoral Researcher with Tongji University, where she is currently an Associate Professor with the College of Electri...Show More
Chengju Liu received the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 2011.
From October 2011 to July 2012, she was a Research Associate with the BEACON Center, Michigan State University, East Lansing, MI, USA. From March 2011 to June 2013, she was a Postdoctoral Researcher with Tongji University, where she is currently an Associate Professor with the College of Electri...View more
Author image of Qijun Chen
Department of Control Science and Engineering, Tongji University, Shanghai, China
Qijun Chen received the B.S. degree in automatic control from the Huazhong University of Science and Technology, Wuhan, China, in 1987, the M.S. degree in control engineering from Xi’an Jiaotong University, Xi’an China, in 1990, and the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 1999, respectively.
He was a Visiting Professor with the University of California, Berkele...Show More
Qijun Chen received the B.S. degree in automatic control from the Huazhong University of Science and Technology, Wuhan, China, in 1987, the M.S. degree in control engineering from Xi’an Jiaotong University, Xi’an China, in 1990, and the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 1999, respectively.
He was a Visiting Professor with the University of California, Berkele...View more
Contents

I. Introduction

It is known that nearly all the physical plants and industrial processes in practice are nonlinear, and these different kinds of nonlinearities impose great difficulties on stability analysis and controller synthesis. During the past few decades, as an effective way to tackle these complex nonlinear systems, fuzzy logic control has received much attention in control community. The fuzzy logic control provides a means of converting a linguistic control strategy based on expert knowledge into an automatic control strategy, and many significant results reported in the literature have shown that it offers an effective method for the control problem of complex nonlinear systems or even nonanalytic systems (refer to [1]–[7] and references therein). To mention a few, in [5] a fuzzy logic controller was designed and implemented on a test vehicle for the lateral motion control, which is modularized as a feedback, preview, and gain scheduling rule bases. The results on stability analysis of continuous-time fuzzy-model-based control systems were reviewed in [2], where some fundamental and essential aspects related to membership-function-dependent analysis methods are summarized. In [6], the problem of robust adaptive fuzzy cooperative tracking control for a class of uncertain nonlinear multiagent systems was studied, which are subject to time delays and dead-zone nonlinearities. For a class of chaotic systems with unknown functions and disturbances, the problem of asymptotic stabilization for such systems were investigated in [7] based on the adaptive fuzzy logic control theory.

Author image of Changzhu Zhang
Department of Control Science and Engineering, Tongji University, Shanghai, China
Changzhu Zhang  (M’11) received the B.S. degree in automation from Qufu Normal University, Rizhao, China, in 2007, the M.S. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2009, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2012.
From March 2013 to February 2014, he was an Associate Research Fellow with the Institute of Advanced Study, Tongji University, Shanghai, China. Since December 2017, he has been a Research Fellow with the Department of Informatics, King's College London, London, U.K. Since 2014, he has been with the College of Electrical and Information Engineering, Tongji University, where he is currently an Associate Professor. His research interests include intelligent control, networked control systems, signal processing, and autonomous driving.
Changzhu Zhang  (M’11) received the B.S. degree in automation from Qufu Normal University, Rizhao, China, in 2007, the M.S. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2009, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2012.
From March 2013 to February 2014, he was an Associate Research Fellow with the Institute of Advanced Study, Tongji University, Shanghai, China. Since December 2017, he has been a Research Fellow with the Department of Informatics, King's College London, London, U.K. Since 2014, he has been with the College of Electrical and Information Engineering, Tongji University, where he is currently an Associate Professor. His research interests include intelligent control, networked control systems, signal processing, and autonomous driving.View more
Author image of Hak-Keung Lam
Department of Informatics, King's College London, London, U.K.
Hak-Keung Lam  (M’98–SM’10) received the B.Eng. (Hons.) and Ph.D. degrees from the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, in 1995 and 2000, respectively.
From 2000 to 2005, he was with the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, as a Postdoctoral Fellow and a Research Fellow. He joined King's College London, London, U.K., as a Lecturer in 2005 and is currently a Reader. He is a Coeditor of two edited volumes: Control of Chaotic Nonlinear Circuits (World Scientific, 2009) and Computational Intelligence and Its Applications (World Scientific, 2012), and Author/Coauthor of three monographs: Stability Analysis of Fuzzy-Model-Based Control Systems (Springer, 2011), Polynomial Fuzzy Model Based Control Systems (Springer, 2016), and Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems (Springer, 2016). His research interests include intelligent control and computational intelligence.
Dr. Lam was a Program Committee Member, International Advisory Board Member, Invited Session Chair, and Publication Chair for various international conferences and a Reviewer for various books, international journals, and international conferences. He is an Associate Editor for IEEE Transactions on Fuzzy Systems, IEEE Transactions on Circuits and Systems II: Express Briefs, IET Control Theory and Applications, International Journal of Fuzzy Systems, and Neurocomputing; and Guest Editor for a number of international journals. He is in the editorial board of a number of international journals.
Hak-Keung Lam  (M’98–SM’10) received the B.Eng. (Hons.) and Ph.D. degrees from the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, in 1995 and 2000, respectively.
From 2000 to 2005, he was with the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, as a Postdoctoral Fellow and a Research Fellow. He joined King's College London, London, U.K., as a Lecturer in 2005 and is currently a Reader. He is a Coeditor of two edited volumes: Control of Chaotic Nonlinear Circuits (World Scientific, 2009) and Computational Intelligence and Its Applications (World Scientific, 2012), and Author/Coauthor of three monographs: Stability Analysis of Fuzzy-Model-Based Control Systems (Springer, 2011), Polynomial Fuzzy Model Based Control Systems (Springer, 2016), and Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems (Springer, 2016). His research interests include intelligent control and computational intelligence.
Dr. Lam was a Program Committee Member, International Advisory Board Member, Invited Session Chair, and Publication Chair for various international conferences and a Reviewer for various books, international journals, and international conferences. He is an Associate Editor for IEEE Transactions on Fuzzy Systems, IEEE Transactions on Circuits and Systems II: Express Briefs, IET Control Theory and Applications, International Journal of Fuzzy Systems, and Neurocomputing; and Guest Editor for a number of international journals. He is in the editorial board of a number of international journals.View more
Author image of Jianbin Qiu
State Key Laboratory of Robotics and Systems, and the Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, China
Jianbin Qiu  (M’10–SM’15) received the B.Eng. and Ph.D. degrees in mechanical and electrical engineering from the University of Science and Technology of China, Hefei, China, in 2004 and 2009, respectively, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Hong Kong, in 2009.
He is currently a Full Professor with the School of Astronautics, Harbin Institute of Technology, Harbin, China. He was an Alexander von Humboldt Research Fellow with the Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg, Germany. His research interests include intelligent and hybrid control systems, signal processing, and robotics.
Dr. Qiu is the Chairman of the IEEE Industrial Electronics Society Harbin Chapter, China. He is an Associate Editor for the IEEE Transactions on Cybernetics.
Jianbin Qiu  (M’10–SM’15) received the B.Eng. and Ph.D. degrees in mechanical and electrical engineering from the University of Science and Technology of China, Hefei, China, in 2004 and 2009, respectively, and the Ph.D. degree in mechatronics engineering from the City University of Hong Kong, Hong Kong, in 2009.
He is currently a Full Professor with the School of Astronautics, Harbin Institute of Technology, Harbin, China. He was an Alexander von Humboldt Research Fellow with the Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg, Germany. His research interests include intelligent and hybrid control systems, signal processing, and robotics.
Dr. Qiu is the Chairman of the IEEE Industrial Electronics Society Harbin Chapter, China. He is an Associate Editor for the IEEE Transactions on Cybernetics.View more
Author image of Chengju Liu
Department of Control Science and Engineering, Tongji University, Shanghai, China
Chengju Liu received the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 2011.
From October 2011 to July 2012, she was a Research Associate with the BEACON Center, Michigan State University, East Lansing, MI, USA. From March 2011 to June 2013, she was a Postdoctoral Researcher with Tongji University, where she is currently an Associate Professor with the College of Electrical and Information Engineering. Her research interests include intelligent control, motion control of legged robots, and evolutionary computation.
Chengju Liu received the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 2011.
From October 2011 to July 2012, she was a Research Associate with the BEACON Center, Michigan State University, East Lansing, MI, USA. From March 2011 to June 2013, she was a Postdoctoral Researcher with Tongji University, where she is currently an Associate Professor with the College of Electrical and Information Engineering. Her research interests include intelligent control, motion control of legged robots, and evolutionary computation.View more
Author image of Qijun Chen
Department of Control Science and Engineering, Tongji University, Shanghai, China
Qijun Chen received the B.S. degree in automatic control from the Huazhong University of Science and Technology, Wuhan, China, in 1987, the M.S. degree in control engineering from Xi’an Jiaotong University, Xi’an China, in 1990, and the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 1999, respectively.
He was a Visiting Professor with the University of California, Berkeley, CA, USA, in 2008. He is currently a Professor with the College of Electronic and Information Engineering, Tongji University. His research interests include network-based control systems and robotics.
Qijun Chen received the B.S. degree in automatic control from the Huazhong University of Science and Technology, Wuhan, China, in 1987, the M.S. degree in control engineering from Xi’an Jiaotong University, Xi’an China, in 1990, and the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 1999, respectively.
He was a Visiting Professor with the University of California, Berkeley, CA, USA, in 2008. He is currently a Professor with the College of Electronic and Information Engineering, Tongji University. His research interests include network-based control systems and robotics.View more
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