Adaptive backstepping non-singular fast terminal sliding mode control for mismatched uncertain systems

An adaptive backstepping non-singular fast terminal sliding mode control is proposed for a class of n-order systems with mismatched uncertainties. For the first n-1 steps, the backstepping method is adopted and uncertain parameters are estimated by using adaptive law, thus the mismatched uncertainties are restrained. A non-singular fast terminal sliding mode is conformed with the integration of the error in the n-th step, and control law is designed to achieve the finite time convergence of the n-th system state. As a whole the system is robust to both matched and mismatched uncertainties. In comparison with the adaptive backstepping terminal sliding method, the proposed control method enhances the convergence rate. Theory analysis proves the stability of the close-loop system, and simulation results show the effectiveness of the proposed method.