High-order fully actuated system approaches: Part III. Robust control and high-order backstepping

Abstract

In this paper, three types of uncertain high-order nonlinear models are firstly proposed, namely, a single high-order fully actuated (HOFA) model with nonlinear uncertainties, an uncertain second-order strict-feedback system (SFS) and an uncertain high-order SFS, and the relations among these types of models are also discussed. Secondly, a direct approach for the design of robust stabilising controllers and robust tracking controllers for an uncertain single HOFA model are proposed based on the Lyapunov stability theory. Using the obtained robust control design result, the second- and high-order backstepping methods for the designs of robust stabilising controllers of the introduced second- and high-order SFSs are also proposed. The proposed approaches do not need to convert the high-order systems into first-order ones, and for a specific system design, the proposed high-order backstepping methods need fewer steps than the usual first-order backstepping method, hence are generally more direct and simpler. An illustrative example demonstrates both the effect and the application procedure of the proposed HOFA robust control approaches.

Keywords:

• High-order fully-actuated models
• high-order backstepping
• high-order strict-feedback systems
• nonlinear uncertainties
• robust control

Acknowledgments

The author is grateful to his Ph.D. students, Tianyi Zhao, Yanmei Hu, Qin Zhao, etc., for helping him with reference selection and proofreading, and particularly to Tianyi Zhao for helping him work out the example.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially supported by the Major Program of National Natural Science Foundation of China [grant numbers 61690210, 61690212], the National Natural Science Foundation of China [grant number 61333003] and the Self-Planned Task of State Key Laboratory of Robotics and System (HIT) [grant number SKLRS201716A].

Notes on contributors

Guangren Duan

Guangren Duan received his Ph.D. degree in Control Systems Sciences from Harbin Institute of Technology, Harbin, P. R. China, in 1989. After a two-year post-doctoral experince at the same university, he became professor of control systems theory at that university in 1991. He is the founder and currently the Director of the Center for Control Theory and Guidance Technology at Harbin Institute of Technology. He visited the University of Hull, the University of Sheffield, and also the Queen's University of Belfast, UK, from December 1996 to October 2002, and has served as Member of the Science and Technology committee of the Chinese Ministry of Education, Vice President of the Control Theory and Applications Committee, Chinese Association of Automation (CAA), and Associate Editors of a few international journals. He is currently an Academician of the Chinese Academy of sciences, and Fellow of CAA, IEEE and IET. His main research interests include parametric control systems design, nonlinear systems, descriptor systems, spacecraft control and magnetic bearing control. He is the author and co-author of 5 books and over 270 SCI indexed publications.