Relay-Switching-Based Fixed-Time Tracking Controller for Nonholonomic State-Constrained Systems: Design and Experiment

Abstract

Dear Editor, This paper investigates the fixed-time trajectory tracking controller design for nonholonomic chained systems with static state constraints. Firstly, a fixed-time tracking control law is given to carry out relay switching, which divides the controller development process into two stages. For the goal of designing fixed-time tracking controller in the second stage and avoiding the explosion of complexity, fixed-time filters are introduced. Under these preparations, a fixed-time tracking controller is elaborated by applying barrier-Lyapunov-function-based backstepping. In addition, a new tracking controller is also proposed to guarantee that the tracking error system is bounded before switching. It has been proved that the resulting closed-loop tracking error system states converge to a small neighborhood around zero within a fixed time and output states are kept in the predefined constrained regions.