Backstepping control for a class of uncertain systems based on non-singular terminal sliding mode

A non-singular terminal sliding mode (TSM) controller design strategy is presented based on backstepping for a class of uncertain nonlinear system. By using a new inverse dynamic TSM surface, a control law with non-singularity is obtained, and the time from any initial system state to reach the sliding mode surface is proved to be finite. In order that the system output can track the expected signal within a finite time, the backstepping design method is introduced after the error variable getting to the sliding mode surface. The Duffing Oscillator is used as a demonstrated example and the simulation results show the good tracking performance and robustness of the proposed controller.