Nussbaum gain adaptive neural asymptotic tracking of nonlinear systems with full-state constraints

Abstract

The adaptive neural tracking control problem of a class of strict-feedback nonlinear systems with unknown control directions (UCD) and full-state constraints is investigated in this paper. The neural network (NN) is adopted to identify the totally unknown nonlinear functions. In the meanwhile, by resorting to the Nussbaum gain technique, the effects caused by the UCD and output dead zone are counteracted. Given physical limits and safety demands, a novel barrier Lyapunov function (BLF)-based adaptive neural control scheme is devised for the strict-feedback nonlinear systems to ensure that the constraints are not violated during operations. Besides, a rigorous theoretical analysis has been given to indicate that all of the closed-loop signals are bounded and the tracking error achieves asymptotic convergence performance. Finally, the effectiveness and flexibility of our proposed scheme are illustrated by two numerical examples.

Keywords:

• Adaptive control
• full-state constraints
• dead zone
• Nussbaum gain technique
• asymptotic tracking control

Data availability statement

The data that support the findings of this study are available on request from the corresponding author.

Disclosure statement

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

Additional information

Funding

This work was supported in part by the Funds of National Science of China [grant number 61973146], [grant number 61773188], [grant number 62173172], and in part by the Distinguished Young Scientific Research Talents Plan in Liaoning Province [grant number XLYC1907077], [grant number JQL201915402].

Notes on contributors

Jin-Zi Yang

Jin-Zi Yang received the B.S. degree in mathematics and applied mathematics from Tangshan Normal University, China, in 2019. She is currently pursuing the M.S. degree with applied mathmatics from the Liaoning University of Technology, Jinzhou, China. Her current research interests include fuzzy control theory, adaptive fuzzy control and nonlinear systems.

Yuan-Xin Li

Yuan-Xin Li received the B.S. degree in mathematics and applied mathematics from Qufu Normal University, China, in 2007, the M.S. degree in computational mathematics from the College of Mathematical Sciences, Dalian University of Technology, Dalian, China, in 2009, and the Ph.D. degree in control theory and control engineering from the College of Information Science and Engineering, Northeastern University, Shenyang, China, in 2017. He is currently a professor in the Department of Science, Liaoning University of Technology, Jinzhou, China. His research interests include adaptive fuzzy/neural control, faulttolerant control, event-triggered control and adaptive control of cyber-physical Systems.