Time Axis Shifting Finite-Gain-Based Prescribed-Time Tracking Control Under Non-vanishing Disturbances

In this article, the prescribed-time tracking control problem for a class of strict-feedback systems with nonvanishing time-varying disturbances is investigated. First, a group of novel disturbance observers are established to observe the disturbances in prescribed time based on time axis shifting finite time-varying gains, and then the state feedback-based control scheme is proposed to realize the prescribed-time tracking control objective upon using the system transformation and adding power integrator technique. The proposed control scheme allows the output of the system to track the reference trajectory in prescribed time and the tracking error maintains zero after that prescribed settling time, making itself different from those most existing prescribed-time control results where the system only exists on the finite time interval based on infinity time-varying gains. The effectiveness of the theoretical results are confirmed by both numerical simulation and experimental studies on Turtlebot3-Burger robot.