Second-order time-varying sliding mode tracking control for uncertain systems

This paper considers the robust tracking control problem of nonlinear singleinput single-output (SISO) systems with parametric uncertainty and disturbance. Firstly, a continuous second-order time-varying sliding mode control (STVSMC) law is proposed. The advantages of the proposed STVSMC are twofold. The global second order sliding mode is established, which implies that the closed-loop system is global robust against matched parameter uncertainty and disturbance. Meanwhile, the chattering problem is significantly alleviated. Then, to guarantee the system error converge to zero in finite time, a finite-time-convergent STVSMC (F-STVSMC) law is presented, where a fast terminal sliding mode item is introduced in the second-order time-varying sliding function design. Finally, the effectiveness of the proposed control strategies is demonstrated by simulation results.