Adaptive finite-time stabilization of nonlinearly parameterized systems subject to mismatching disturbances

This paper gives a first try to the finite-time control for nonlinear systems with unknown parametric uncertainty and external disturbances. The serious uncertainties generated by unknown parameters are compensated by skillfully using an adaptive control technique. Exact knowledge of the upper bounds of the disturbances is removed by employing a disturbance observer-based control method. Then, based on the disturbance observer-based control, backstepping technique, finite-time adaptive control, and Lyapunov stability theory, a composite adaptive state-feedback controller is strictly designed and analyzed, which guarantees the closed-loop system to be practically finite-time stable. Finally, both the practical and numerical examples are presented and compared to demonstrate the effectiveness of the proposed scheme.