Finite-Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite-time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite-time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite-time controller to guarantee the excellent robustness of the closed-loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed-loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite-time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.