Adaptive backstepping-based terminal-sliding-mode control for uncertain nonlinear systems

An adaptive backstepping-based terminal-sliding-mode control method is proposed for a class of uncertain nonlinear systems in parametric-strict feedback form.The adaptive control law is combined with the first n-1 steps of the backstepping method to estimate the unknown parameters of the system.In the n-th step,a nonsingular terminal-sliding-mode is then utilized to drive the last state of the system to converge in a finite period of time.Furthermore,the derivative estimator is used to obtain the derivatives of the states of the error system;and the high-order sliding-mode-control law is designed to eliminate the chattering and to make the system robust to both the matched and the mismatched uncertainties.Compared to the adaptive backstepping-based linear sliding-mode-control method,the proposed method improves the convergence rate and the steady-state tracking accuracy of the system,and makes the control signal smoother.Finally,the simulation results are presented to validate the method.