second order sliding mode control with finite time convergence

in this paper, a new smooth second order sliding mode control is proposed. this algorithm is a modified form of super twisting algorithm. the super twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular lyapunov function. the proposed algorithm which is able to control nonlinear systems with matched structured uncertainty, is able to guarantee the finite time stability. the main advantage of this second order sliding mode control is reaching to sliding surface with high precision without chattering in control signal. in simulation section, the proposed algorithm is compared with the boundary layer sliding mode control and then is applied to designing a finite time nonlinear guidance law that is robust with respect to target maneuvers. simulation results show that the control input in this algorithm is smooth and has no chattering and by applying this method, sliding variables will converge to zero in a given desired finite time.