Global prescribed-time control of a class of nonholonomic systems by time-varying dynamic feedback

In this paper, the global prescribed-time control problem of a class of nonholonomic systems with time-varying drift terms is investigated. By using time-varying high-gain function, a novel time-varying oscillator-like differential equation is constructed. Then with the aid of the auxiliary state generated by such an equation, time-varying dynamic feedback controllers are proposed for the (high-order) extended Heisenberg systems. It is proved that the state of the closed-loop system converges to zero at any prescribed time and the controls are bounded. As applications, the prescribed-time control problems for two physical systems are studied. Numerical simulations verify the effectiveness of the proposed methods.