Output feedback stabilization within prescribed finite time of asymmetric time-varying constrained nonholonomic systems

In this article, the fixed-time stabilization problem is investigated for a category of nonholonomic chained-form systems. Notably, the study possess two important features: the system under investigation is subject to asymmetric time-varying output constraints (that are equal to the space constraints of mobile robot or other nonholonomic mechanical systems), and only output is available for feedback. A novel universal barrier Lyapunov function (UBLF), which is equivalent to the classical Lyapunov function for unconstrained systems, is introduced to address asymmetric time-varying output constraint requirements. Under the universal framework in the sense that the proposed scheme can work for system with symmetric/asymmetric constraints or without constraint requirements, an output feedback controller is developed by employing the barrier function and the bi-limit control techniques. It is shown that the suggested controller ensures the states of the closed-loop system (CLS) to zero in a prescribed finite time, while the asymmetric time-varying constraints on system output are not violated. Finally, simulation results are given to confirm the efficacy of the presented control scheme.