The planar engagement between a maneuvering target and a homingmissile is considered. It is assumed that once during the engagementthe missile carries out a switch 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 byapplying the approach of hybrid differential games. The particular casewhere both the missile and the target have first-order strictly properdynamics, and the missile, exploiting the Proportional Navigation guid-ance law, changes its gain once during the engagement, is elaborated.Numerical examples are presented.
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