Adaptive backstepping-based NTSM control for unmatched uncertain nonlinear systems

An adaptive backstepping-based non-singular terminal sliding mode（NTSM） control method is proposed for a class of uncertain nonlinear systems in the parameteric-strict feedback form. The adaptive control law is combined with the first n- 1steps of the backstepping method to estimate the unknown parameters of the system. In the nth step, an NTSM control strategy is utilized to drive the last state of the system to converge in a finite time. Furthermore, the derivate estimator is used to obtain the derivates of the states of the error system; the higher-order non-singular terminal sliding mode control（HONTSMC） law is designed to eliminate the chattering and make the system robust to both matched and unmatched uncertainties. Compared to the adaptive backstepping-based linear sliding mode control method（LSMC）, the proposed method improves the convergence rate and the steady-state tracking accuracy of the system, and makes the control signal smoother. Finally, the compared simulation results are presented to validate the method.