Adaptive backstepping-based NTSM control for unmatched uncertain nonlinear systems

An adaptive backstepping-based non-singular termi- nal 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 - 1 steps of the backstepping method to estimate the unknown pa- rameters 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 de- signed 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.