Lyapunov-basedAdaptive SmoothSecond-order Sliding Mode Guidance Law with Proving Finite Time Stability

A new adaptive smooth second-order sliding mode control is proposed for uncertain nonlinear systems in this paper. The finite time stability is proved using a Lyapunov technic. The proposed controller consists of an adaptive term equal to the uncertainty in finite time. This algorithm is used to design terminal guidance law for homing interceptors to intercept maneuvering targets. The guidance law generates smooth acceleration commands and the control signal is able to stabilize relative lateral velocity in a desired time. Finally, the proposed guidance law is compared with the second-order sliding mode guidance law from carried out simulations.