Adaptive finite-time control for uncertain nonlinear systems with application to mechanical systems

In this paper, an adaptive fuzzy finite-time control scheme is proposed for a class of nonlinear systems with unknown nonlinearities via backstepping technique. Fuzzy logic systems are employed to approximate the unknown continuous functions. Under some appropriate assumptions, it is proved that if the designed parameters in the controller and adaptive laws are suitably chosen, the proposed scheme can guarantee that the state of the closed-loop system converges to a small neighborhood of the origin in finite time. Moreover, the design strategy is successfully applied to solve the problem of finite-time tracking for a class of mechanical systems.