Adaptive fuzzy control with smooth inverse for nonlinear systems preceded by non-symmetric dead-zone

Abstract

In this study, the adaptive output feedback control problem of a class of nonlinear systems preceded by non-symmetric dead-zone is considered. To cope with the possible control signal chattering phenomenon which is caused by non-smooth dead-zone inverse, a new smooth inverse is proposed for non-symmetric dead-zone compensation. For the systematic design procedure of the adaptive fuzzy control algorithm, we combine the backstepping technique and small-gain approach. The Takagi–Sugeno fuzzy logic systems are used to approximate unknown system nonlinearities. The closed-loop stability is studied by using small gain theorem and the closed-loop system is proved to be semi-globally uniformly ultimately bounded. Simulation results indicate that, compared to the algorithm with the non-smooth inverse, the proposed control strategy can achieve better tracking performance and the chattering phenomenon can be avoided effectively.

Keywords:

• dead-zone
• smooth inverse
• adaptive control
• fuzzy control
• nonlinear systems

Acknowledgements

The authors would like to thank the anonymous reviews for their constructive comments and valuable suggestions which greatly improve the presentation of this paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51305011]; the National Basic Research Program of China (973 Program) [grant number 2014CB046402] and the Fundamental Research Funds for the Central Universities [grant number YWF-14-FGC-016], [grant number YWF-13-T-RSC-064].

Notes on contributors

Xingjian Wang

Xingjian Wang received the PhD and BEng degrees in mechatronics engineering from Beihang University, China, in 2012 and 2006. From 2009 to 2010, he was a visiting scholar in the School of Mechanical Engineering, Purdue University, West Lafayette, IN. He is currently with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His research interests include adaptive and nonlinear control, fault diagnostic, prognostic and health management, active fault tolerant control.

Shaoping Wang

Shaoping Wang received the PhD, MEng and BEng degrees in mechatronics engineering from Beihang University, China, in 1994, 1991 and 1988. She has been with the Automation Science and Electrical Engineering at Beihang University since 1994 and promoted to the rank of professor in 2000. She was honoured as a Changjiang scholar orofessor by the Ministry of Education of China in 2013. Her research interests include engineering reliability, fault diagnostic, prognostic and health management, active fault tolerant control.