A realistic aerial combat duel as a differential game study

Optimal control theory is applied to a realistic missile duel between two aircraft on nonshort range. The duel is formulated as a two person, zero-sum differential game with perfect information and free final times. The longitudinal acceleration of each vehicle is modelled in accordance with realistic aircraft and long range missiles, including practical constraints like maximum loadfactor due to stall or structural limit. Accordingly the differential game will be very non-linear and an effective numerical optimization method is needed. By a modified differential dynamic programming method combined with an expedient convergence, control technique the problem has successfully been solved. However, the duel problem has a particular property by the launch mechanism, which the ordinary control theory does not include. Therefore the algorithm used is extended to a new type of transversality condition. A discussion of applying differential game theory in practice is made. This is demonstrated in two examples, one having four stationary solutions.