Ellis Jeffrey Lee. A problem of allocation of supporting fire in combat as a zero sum differential game

Monterey, California: U.S. Naval Postgraduate School, 1974. — 60 p.Optimal fire-support strategies are studied through a deterministic differential game using Lanchester-type equations of warfare. In addition to the MAX-MIN principle, the theory of singular extremals is required to solve this prescribed duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to the optimal fire-support strategy of the attacker requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). Numerical examples are given. The military significance (based on the marginal value interpretation of the dual variable) of various optimality conditions is discussed.