Family of Local Solutions in a Missile-Aircraft Differential Game

To date many studies of missile and aircraft differential games seem to have tried to find a unique solution, however, the authors of this study found there are many solutions of comparable values to the game. The authors called them "a family of local solutions." This paper shows a method to find the family for a missile and an aircraft differential game, which minimizes and maximizes the essential payoff of the problem, the miss distance, without employing any linearized approximation. For this purpose, the authors introduced the concept of energy maneuverability. The sets of optimal terminal surfaces of both vehicles that maximize their velocities are obtained first. Next, minimax solutions of the vehicles that start from these terminal surfaces, and minimize and maximize the miss distance, respectively, are calculated; then a local minimax family in this game is obtained. The proposed method can solve minimax problems under several vehicles' acceleration constraints. The results may be able to be incorporated into an actual missile guidance system as a knowledge base, and then the performance will be significantly improved.