Adaptive stabilisation of second-order strict-feedback systems based on FAS with tuning functions

Abstract

This paper thoroughly investigates adaptive stabilisation for a specific class of second-order strict-feedback nonlinear systems. Drawing inspiration from the fully actuated system (FAS) approach, an adaptive control scheme incorporating FAS with tuning functions is proposed. Notably, this approach directly addresses second-order systems without the need for reducing them to first-order systems, streamlining the intricate procedures involved. To handle uncertain parameters within the system, a combined scheme of adaptive estimation and tuning functions is employed. Rigorous analysis using Lyapunov stability theory demonstrates that the designed controller ensures the system's asymptotic convergence to the equilibrium point, with all other signals in the closed-loop system bounded. Finally, two simulation experiments verify the effectiveness of the proposed strategy: numerical simulations compared with sliding mode control and backstepping control, and practical application on the single-link robotic arm with a comparative analysis against backstepping control.

Keywords:

• Fully actuated systems
• adaptive control
• tuning functions
• single-link robotic arm

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the China Postdoctoral Science Foundation [grant number 2022M721902], in part by the Guangyue Young Scholar Innovation Team of Liaocheng University [grant number LCUGYTD2022-01], in part by the Liaocheng University Major Vertical Project Cultivation Plan Project [grant number 318062305] and in part by the Science Center Program of National Natural Science Foundation of China [grant number 62188101].

Notes on contributors

Xueqi Wu

Xueqi Wu received the B.S. degree in Data Science and Big Data Technology from Liaocheng University, Liaocheng, China, in 2022, where she is currently pursuing the M.S. degree with the School of Mathematics Science. Her research interests include nonlinear system control and adaptive control.

Wei Sun

Wei Sun (Senior Member, IEEE) received the M.S. degree in automatic engineering from Qufu Normal University, Qufu, China, in 2011, and the Ph.D. degree in automatic control from Southeast University, Nanjing, China, in 2014. From 2018 to 2019, he was a Post-Doctoral Researcher with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan. He is currently an Associate Professor with the School of Mathematics Science, Liaocheng University, Liaocheng, China. His current research interests include nonlinear control, adaptive fuzzy control, and robotics. He serves as an Associate Editor for Information Sciences and International Journal of Fuzzy Systems.

Xudong Zhao

Xudong Zhao (Senior Member, IEEE) received the B.S. degree in automation from the Harbin Institute of Technology, Harbin, China, in 2005, and the Ph.D. degree in control science and engineering from the Space Control and Inertial Technology Center, Harbin Institute of Technology, in 2010. He was a Lecturer and an Associate Professor with the China University of Petroleum, Beijing, China. In March 2013, he was a Professor with Bohai University, Jinzhou, China. In 2014, he was a Post-Doctoral Fellow with the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong. Since December 2015, he has been with the Dalian University of Technology, Dalian, China, where he is currently a Professor. His research interests include switched systems, positive systems, multiagent systems, fuzzy systems, and their applications. He received the 2017 and 2018 Highly Cited Researcher Award. He serves as an Associate Editor for the IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS: SYSTEMS, Nonlinear Analysis: Hybrid Systems, Neurocomputing, IEEE ACCESS, International Journal of General Systems, Chinese Journal of Aeronautics, and Acta Automatica Sinica. He has been granted as the Outstanding Reviewer for Automatica, IET Control Theory and Applications, and Journal of the Franklin Institute.