New results on robust tracking control for a class of high-order nonlinear time-delay systems

Abstract

This paper considers the global tracking control problem for a class of nonlinear systems. Compared with the existing results, one significant distinction of this work is that it allows the high-order powers, zero dynamics, time-delay and external disturbances. By constructing a new Lyapunov–Krasovskii (L–K) functional and using the modified adding a power integrator method, we successfully design a non-smooth tracking controller which guarantees that all the signals of the closed-loop system are bounded. The tracking error can be adjusted small enough using the designed parameters. As a practical application, in the simulation, the single-link robot system is studied to show the validness of the strategy.

Keywords:

• Nonlinear time-delay systems
• disturbances
• tracking control
• adding a power integrator method

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Zongyao Sun http://orcid.org/0000-0002-2102-9588

Additional information

Funding

This work is supported by National Nature Science Foundation of China [grant numbers 61603231, 61773237 and 61873120], Youth Science and Technology Research Foundation of the ShanXi Science and Technology Department of China [grant number 201801D221167], Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (STIP) [grant numbers 2019L0492 and 2019L0011] and Youth Research Foundation Project of Shanxi University of Finance and Economics [grant number QN-2019018].

Notes on contributors

Lingrong Xue

Lingrong Xue received her M.S. degree from Qufu Normal University, Qufu, China, in 2015 and the Ph.D. degree in Shandong University of Science and Technology, Qingdao, China, in 2018. She is currently a Lecturer in School of Information, Shanxi University of Finance and Economics, Taiyuan, China. Her main research interests include high-order nonlinear time-delay system, stabilisation control, adaptive control and robust tracking control.

Zhenguo Liu

Zhenguo Liu received his M.S. degree from Qufu Normal University, Qufu, China, in 2012 and the Ph.D. degree from Southeast University, Nanjing, China, in 2015. He is currently an Assistant Professor in the Department of Automation, Shanxi University, Taiyuan, China. His research interests cover nonlinear system control, nonholonomic system control and stability theory of time-delay systems.

Zongyao Sun

Zongyao Sun received the M.S. and Ph.D. degrees from Qufu Normal University and Shandong University, China, in 2005 and 2009, respectively. Currently, he is a Professor in Institute of Automation, Qufu Normal University, Qufu, China. His current research interests include nonlinear control, adaptive control and stability theory of time-delay systems.

Wei Sun

Wei Sun received the M.S. degree from Qufu Normal University, Qufu, China, in 2011, and the Ph.D. degree from Southeast University, Nanjing, China, in 2014. He is currently a Post-Doctoral Researcher with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan. His current research interests include nonlinear system control, adaptive fuzzy control and robotics.