Fuzzy adaptive asymptotic tracking of uncertain nonlinear systems with full states constraints

ABSTRACT

In this paper, the fuzzy adaptive tracking control problem is studied for a class of nonlinear strict feedback systems with time-varying full state constraints. For the full state constraints problem, the nonlinear transformation function is used to transform the constraint problem into a non-constraint problem. A new adaptive control framework is proposed for asymptotic tracking of nonlinear systems with unknown virtual control coefficients (UVCC). Under the proposed control scheme, the effects of UVCC and unknown nonlinear functions are compensated by the introduction of some well-defined smoothing functions and boundary estimation methods. In addition, a new Lyapunov function is constructed, which successfully achieves the tracking error of the closed-loop system converge to zero and all the signals in the closed-loop systems are bounded. In the meanwhile, all states are always keep in their asymmetric time-varying constraints. Finally, a numerical example is presented to show the effectiveness of the proposed control scheme.

Keywords:

• Uncertain nonlinear systems
• fuzzy logic systems (FLS)
• backstepping design
• adaptive control
• asymptotic tracking control
• full-state constraints

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 No. 61973146, 61603166), in part by the Doctoral Research Initiation of Foundation of Liaoning Province,China (No. 20180540047), in part by the Distinguished Young Scientific Research Talents Plan of Liaoning Province, China (No.XLYC1907077, JQL201915402), and in part by the Taishan ScholarProject of Shandong Province of China (Grant No. tsqn201909097).

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, fault-tolerant control, event-triggered control and adaptive control of cyber-physical Systems.