Hybrid evasion strategy against a missile with guidance law of variable structure

The planar engagement between a maneuvering target and a homing missile is considered. It is assumed that once during the engagement, the missile switches from one linear guidance law to another. This leads to a formulation of a hybrid evasion problem for the target. The optimal evasion strategy in the hybrid problem is constructed by applying the approach of hybrid differential games. It is different than the concatenation of the evasion strategies that are optimal for each individual mode. The particular case where both the missile and the target have first-order strictly proper dynamics, and the missile, exploiting the Proportional Navigation guidance law, changes its gain once during the engagement, is elaborated. Numerical examples are presented.