Robust adaptive tracking control of MIMO nonlinear systems in the presence of actuator hysteresis

Abstract

Adaptive tracking control of a class of MIMO nonlinear system preceded by unknown hysteresis is investigated. Based on dynamic surface control, an adaptive robust control law is developed and compensators are designed to mitigate the influences of both the unknown bounded external uncertainties and the unknown Prandtl–Islinskii hysteresis. By adopting the low-pass filters, the explosion of complexity caused by tedious computation of the time derivatives of the virtual control laws is overcome. With the proposed control scheme, the closed-loop system is proved to be semi-globally ultimately bounded by the Lyapunov stability theory, and the output of the controlled system can track the desired trajectories with an arbitrarily small error. Finally, numerical simulations are given to verify the effectiveness of the proposed approach.

Keywords:

• nonlinear MIMO system
• Prandtl–Islinskii hysteresis
• dynamic surface control
• adaptive control

Acknowledgements

The authors are also thankful to the anonymous referees for their helpful comments.

Additional information

Funding

This paper is partly supported by the National Science Foundation of China [grant number 61025016], [grant number 61473183], [grant number 61034008], [grant number 61221003], [grant number 61273116]; Program of Shanghai Subject Chief Scientist [grant number 14XD1402400]; SJTU M&E Joint Research Foundation [grant number YG2013MS04].

Notes on contributors

Guiyuan Fu

Guiyuan Fu is currently a PhD candidate in control theory and control engineering with Department of Automation, Shanghai Jiaotong University. He received his B.S. degree and M.S. degree in 2007 and 2010, respectively. His research interests include robust control of nonlinear system, complex system, opinion dynamics based on agent system.

Linlin Ou

Linlin Ou received her PhD degree in control theory and control engineering from Department of Automation, Shanghai Jiaotong University, China in 2006. She is currently a professor at the College of Information Engineering, Zhejiang University of Technology. Her research interests focus on theoretical aspects of time-delayed control systems, robot control, multi-agent system and cooperative control.

Weidong Zhang

Weidong Zhang received his BS, MS and Ph.D. degrees from Zhejiang University, Hangzhou, China, in 1990, 1993 and 1996, respectively. He worked with the National Key Laboratory of Industrial Control Technology as a post-doctor before joining Shanghai Jiao Tong University, Shanghai, China, in 1998 as an associate professor. Since 1999, he has been a professor at the Department of Automation, Shanghai Jiao Tong University. He served as the deputy dean of the Department of Automation, Shanghai Jiao Tong University. He has authored or co-authored over 200 journal and conference papers. His research interests include robust control, distributed control and their applications in industry.