Finite-time convergent terminal guidance law design based on stochastic fast smooth second-order sliding mode

A novel finite-time convergent terminal guidance law, based on stochastic fast smooth second-order sliding mode control theory, is proposed in order to handle the track imprecision caused mainly by inertial lag, model uncertainties and atmospheric environment disturbances, as well as the stochastic noise caused by target maneuver term. The missile-interceptor guidance system against targets performing evasive maneuvers is considered. The target maneuver model is employed to alleviate the dependence of the perfect knowledge of the range to target and the range rate as well as the limitation to target normal acceleration. Considering that the system is driven by additive noise, which do not have any equilibrium, a new concept of finite-time mean-square practical convergence is presented. And based on this concept, the finite-time convergence property of proposed guidance law is deduced. The availability and effectiveness of the proposed guidance law is illustrated through computer simulations. The results show that the proposed guidance law can realize finite-time convergence, and it has strong robustness against bounded uncertainties as well as the stochastic noise. The proposed guidance law does not has violent high-frequency chattering, which guarantees the tracking accuracy.