Implementation of optimal guidance laws using predicted missile velocity profiles

A class of weighted control-effort minimizing guidance laws are derived for missiles of varying velocity. As a practical weighting function, we consider a function of air density and missile velocity parameterized by positive real numbers. The resulting optimal guidance problem can be interpreted as the drag minimization problem for subsonic or supersonic missiles, depending on what parameters are used. This approach is extended easily to solve the drag minimization of a typical antiaircraft missile system with an arbitrary velocity profile and arbitrary drag characteristics, as demonstrated by a simulation study. We also present analytical results on how the guidance gain of the optimal law varies according to the values of the parameters. Because the optimal guidance laws make use of the future missile velocity profile, one critical issue is how to implement the laws. To avoid the difficulty that an inaccurately predicted missile velocity profile causes the guidance command to blow up in the last part of the engagement, we suggest two simple on-line velocity-profile updating schemes, which considerably alleviate the problem.