Finite-Time Control of a Class of Nonlinear Underactuated Systems with Application to Underactuated Axisymmetric Spacecraft

In this paper, the finite-time control problem of a class of nonlinear underactuated systems is addressed. By using the auxiliary state generated by a time-varying oscillator-like differential equation and constructing a novel Lyapunov-like function, a time-varying dynamic feedback controller is designed for such nonlinear underactuated systems. It is proved that the state of the closed-loop system converges to zero at the finite time and the controls are bounded. As an application, the finite-time tracking problem for underactuated axisymmetric systems is solved. Numerical simulations verify the effectiveness of the proposed methods.