Stabilizing the second-order nonholonomic systems with chained form by finite-time stabilizing controllers

An underactuated mechanical system is generally a good test bed for advanced nonlinear controllers and can be applied to design a novel mechanical system with better energy efficiency and good controllability. It has been shown that the dynamics of many underactuated mechanical systems could be transformed into the chained canonical form. To improve the performance of the controllers presented in the literature, a novel controller design method is proposed in this paper. It is shown that the set-point stabilization problem of the second-order chained form systems can be changed into a trajectory-tracking problem based on the nonsmooth Holder continuous feedback. By designing the tracked trajectory, the presented controller permits the achievement of exponential stability. Some numerical simulations demonstrate the stability of the proposed controller for an underactuated Hovercraft system.