Perfect tracking control of discrete-time quadratic TS fuzzy systems via feedback linearisation

ABSTRACT

Perfect tracking control is an important and frequently encountered requirement in various industries (e.g. robotic control). We developed a novel systematic framework for designing a fuzzy controller via feedback linearisation to control a class of discrete-time Takagi–Sugeno (TS) fuzzy systems with quadratic rule consequents to achieve such tracking. We established a necessary condition for its local stability and a necessary and sufficient condition for the boundedness of the controller. The feedback linearisation is known to fail to work in certain systems due to the unboundedness of the tracking controller output. To address this issue, we developed a method to check whether any given quadratic TS fuzzy system will cause such a failure. We developed a scheme to ensure that the output of the controller designed for any failure-causing system will be bounded and the resulting controller will attain nearly perfect tracking performance. Applying feedback linearisation to the quadratic fuzzy systems is innovative relative to the literature exclusively dealing with the TS fuzzy systems with linear rule consequents (including our previous results), which are now generalised by the new findings. Two numerical examples are provided to illustrate the effectiveness and utility of our new theoretical results.

KEYWORDS:

• Discrete-time quadratic TS fuzzy systems
• perfect tracking control
• feedback linearisation
• stability analysis
• Lyapunov’s linearisation method

ORCID

Liwei Ren http://orcid.org/0000-0002-1928-5742

Hao Ying http://orcid.org/0000-0002-4891-6785

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under grant numbers 61304006 and 61273095.

Notes on contributors

Xiaojun Ban

Xiaojun Ban was born in Xi’an, Shaanxi province, China, in 1978. He received the B.S. degree in automation from Harbin Engineering University in 2001, Harbin, China, and the M.S. and Ph.D. degrees in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2003 and 2006, respectively. He is currently a Professor with the Center for Control Theory and Guidance Technology, Harbin Institute of Technology. At HIT, he teaches the following graduate course: System identification and adaptive control, as well as the following undergraduate course: Fuzzy control. His current research interests include fuzzy control, linear parameter-varying control and gain-scheduling control. E-mail: [email protected].

Liwei Ren

Liwei Ren was born in Shuangcheng, Heilongjiang province, China, in 1989. She received the B.S. degree in automation from Yanshan University, Qinhuangdao, China, in 2011 and the M.S. degree in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2013. She is currently working toward the Ph.D. degree with the Center for Control Theory and Guidance Technology, Harbin Institute of Technology. Her current research interests include fuzzy systems and control and system identification. E-mail: [email protected].

Zhibin Yan

Zhibin Yan was born in Hanchuan, Hubei province, China, in 1967. He received the B.S. degree from Nankai University, Tianjin, China, in 1988, and the M.S. and Ph.D. degrees from Harbin Institute of Technology, Harbin, China, in 1991 and 2002, respectively, all in Mathematics. Since 1991, he has been with Harbin Institute of Technology, where he is presently a professor in the Center for Mathematics and Interdisciplinary Sciences. His current research interests include differential-algebraic equation, control under communication constraint, system identification, and state estimation of stochastic system. E-mail: [email protected].

Hao Ying

Hao Ying was born in Shanghai, China, in 1958. He received the B.S. degree in electrical engineering and the M.S. degree in computer engineering from Donghua University, Shanghai, in 1982 and 1984, respectively, and the Ph.D. degree in biomedical engineering from the University of Alabama at Birmingham, USA, in 1990. He is currently a Professor with the Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI, USA. He has two books, 107 peer-reviewed journal papers and over 160 peer-reviewed conference papers. He is serving as an Associate Editor or a Member of Editorial Board for nine international journals, including the IEEE Transactions on Fuzzy Systems and the IEEE Transactions on Systems, Man, and Cybernetics: Systems. He serves as a member of the Fuzzy Systems Technical Committee of the IEEE Computational Intelligence Society and is a member of the 2017 Fellow Evaluation Committee of the IEEE Systems, Man, and Cybernetics Society. He also served as a Program/Technical Committee Member for over 90 international conferences. E-mail: [email protected].