Nonlinear mapping-based fixed-time stabilization of uncertain nonholonomic systems with time-varying state constraints

• Published in: Journal of the Franklin Institute Vol. 357; no. 11; pp. 6653 - 6670
• Main Authors: Gao, Fangzheng, Huang, Jiacai, Shi, Xinxin, Zhu, Xiaochun
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.07.2020; Elsevier Science Ltd
• Subjects: Control theory; Feedback control; Liapunov functions; Mapping; Mathematical functions; Mechanical systems; Microelectromechanical systems; Stabilization; State feedback; Switching
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.04.028

In this paper, the problem of fixed-time stabilization (FxTS) is addressed for a type of uncertain chained-form nonholonomic systems. Remarkably, the study possess two important features: one is that the system under investigation is subject to time-varying state constraints (that are equal to the space constraints of mobile robot or other nonholonomic mechanical systems), and the other is that the design control laws can render the closed-loop system (CLS) states to zero in any prescribed finite time. A novel nonlinear mapping (NM) is introduced to cope with time-varying state constraints. With the help of the adding a power integrator technique and the reasonable switching control strategy, this paper proposes a fixed-time state feedback controller, and completes the performance analysis based on the construction of integral Lyapunov function. Finally, a simulation example is presented to confirm the effectiveness of control strategy.