A novel backstepping sliding mode dynamic surface control

A novel backstepping sliding mode control with guaranteed L_∞ tracking performance is proposed for a class of typical uncertain strict-feedback nonlinear systems. Inspired by dynamic surface control, the introduction of a low-pass filter avoids the problem of explosion of terms in traditional backstepping design, and instead of the sign function in the sliding mode controller, a continuously differentiable hyperbolic tangent function is used to eliminate the chattering in sliding mode control. Semi-global stability of the closed-loop system is proved based on Lyapunov stability theory. By appropriately choosing design parameters and initializing error variables, the exact relationship between L_∞ performance of the tracking error and designing parameters is established, and the L_∞ performance of the tracking error is guaranteed. Simulation results demonstrate the effectiveness of the proposed approach.