Citation

Ardema MD, Heymann M, Rajan N. Math. Model. 1987; 8: 13-14.

Copyright

(Copyright © 1987, Elsevier Publishing)

DOI

10.1016/0270-0255(87)90530-6

PMID

unavailable

Abstract

Combat is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives. With each opponent is associated a target in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously or in neither, a joint capture or a draw, respectively, is said to occur. Resolution of the encounter is formulated as a combat game; namely, as a pair of competing event-constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero-sum-differential game. Otherwise, the optimal strategies are computed from a resulting non-zero-sum game. Since optimal combat strategies frequently may not exist, approximate combat games are also formulated leading to approximate optimal strategies. To illustrate combat games, an example, called the turret game, is considered. This game may be thought of as a highly simplified model of air combat, yet it sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit-evasion games.