Three-dimensional optimal pursuit and evasion with bounded controls

The missile-aircraft pursuit-evasion problem is formulated by a three-dimensional linearized kinematic model with bounded control. The formulation is valid both for the optimal control (against a known adversary strategy) and the zero sum differential game versions. Assuming perfect information, the linearized kinematic model yields for both versions a solution which can be impletemented in real time for airborne application. The avoidance of a known pursuer by an evader who has no state information is solved by a stochastically optimal periodical maneuver. Other examples of imperfect information are briefly discussed.