Input and output constraints-based stabilisation of switched nonlinear systems with unstable subsystems and its application

ABSTRACT

This paper studies the problem of stabilisation of switched nonlinear systems with output and input constraints. We propose a recursive approach to solve this issue. None of the subsystems are assumed to be stablisable while the switched system is stabilised by dual design of controllers for subsystems and a switching law. When only dealing with bounded input, we provide nested switching controllers using an extended backstepping procedure. If both input and output constraints are taken into consideration, a Barrier Lyapunov Function is employed during operation to construct multiple Lyapunov functions for switched nonlinear system in the backstepping procedure. As a practical example, the control design of an equilibrium manifold expansion model of aero-engine is given to demonstrate the effectiveness of the proposed design method.

KEYWORDS:

• Switched nonlinear systems
• nested switching controllers
• output constraint
• bounded input

Acknowledgment

The authors would like to thank the editor andthe anonymous reviewers for their valuable comments and suggestions that have improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61233002]; the 111 Project [grant number B16009]; IAPI Fundamental Research Funds [grant number 2013ZCX03-01].

Notes on contributors

Chao Chen

Chao Chen was born in 1981. He received the B.S. degree in automation from Harbin Institute of Technology, Harbin, China, in 2004, and the M.S. and Ph.D. degrees in control theory and applications from Northeastern University, Shenyang, China, in 2008 and 2017, respectively. His main research interests include switched systems, hybrid control, and aero-engine control systems.

Qian Liu

Qian Liu was born in 1989. She received the B.S. degree from Beijing Information Science and Technology University, Beijing, China, in 2011 and the M.S. degree in Mathematics in 2013 from Northeastern University, Shenyang, China.  From September 2015 to September 2017, she was a joint Ph.D. student at the University of Notre Dame. She is currently working toward the Ph.D. degree at the College of Information Science and Engineering, Northeaster University. Her research interests include switched systems and hybrid control.

Jun Zhao

Jun Zhao was born in 1957. He received the B.S. and M.S. degrees in mathematics from Liaoning University, Shenyang, China, in 1982 and 1984, respectively, and the Ph.D. degree in control theory and applications from Northeastern University, Shenyang, in 1991. Since 1994, he has been with the College of Information Science and Engineering, Northeastern University, where he is currently a Professor and was a Postdoctoral Fellow from 1992 to 1993. From February 1998 to February 1999, he was a Senior Visiting Scholar at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign. From November 2003 to May 2005, he was a Research Fellow in the Department of Electronic Engineering, City University of Hong Kong. Since November 2006, as a Fellow, he has been with the Research School of Information Sciences and Engineering, The Australian National University. His main research interests include switched systems, hybrid control, nonlinear systems, and robust control.