On the approximate solution of complex combat games

We view air-to-air combat as a two-target differential game between armed opponents. Although it is presently beyond the state of the art to solve for the optimal controls for both of the opponents, we can constrain the game to searching for each initial condition for the guidance law for each opponent from the sets of those considered. This constraint changes evaluation of the game to that of a discrete game, which can be solved by enumeration. As an example, a one-on-one two-dimensional air-to-air combat game has been designed. The game includes both attack and evasion guidance laws for both aircraft. To decide which of the guidance laws to use, the quantized initial-condition space is flooded with four simulated fights for each initial condition, depicting the strategies for the two opponents: attack-attack, attack-evasion, evasion-attack, and evasionevasion, and the outcomes are recorded. For each initial condition, the minimax procedure from discrete games selects the best choice from the available strategies for both players. The results are feedback and outcome charts that can be used to turn one of the automatic opponents into an intelligent opponent against a human pilot.