Linear-quadratic pursuit-evasion differential games are considered where the cost is a weighted combination of the pursuer's control effort, the evader's control effort, the miss distance and the terminal lateral velocity. The analysis is done for planar motion at constant speed, and the kinematics are first linearized around a nominal collision course. Closed-form optimal strategies are formulated for both players. Some known strategies are shown to be special cases of this problem. Numerical results for a zero miss-distance case with different weights for the terminal lateral velocity are presented. In the case of zero miss distance and zero terminal lateral velocity, closed-form expressions for the optimal trajectories are obtained.
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