Abstract: To control the impact time for a missile, the problem of impact time control guidance considering the stationary target and the moving target with constant velocity is studied in terms of the engagement geometry. According to a theoretical formula of the missile lead angle aiming at the stationary target, a sliding mode switching surface is constructed via the tracking error of the lead angle. An impact time control guidance law without singularity is designed based on the terminal sliding mode control theory. The convergence and the range of values allowed for the guidance parameter are theoretically analyzed. It is rigorously proved that the proposed guidance law satisfies the Lyapunov stability criterion and has no singularity. By utilizing the method of interception point prediction, this guidance law is extended to adapt to the case with a constant velocity target. The effectiveness of the proposed impact time control guidance law is validated through an amount of numerical simulations under various conditions.

Key words: missile, guidance law, impact time control, terminal sliding mode theory, lead angle