Fire distribution in Lanchester inertial combat, I: "Square-law" attrition of target types

Abstract

The influence of command and control limitations on fire distribution tactics for a homogeneous force in combat against heterogeneous enemy forces is studied through a deterministic optimal control problem. Lanchester-type equations for a square law attrition process are used to model the combat. Command and control limitations are incorporated into the model through upper and lower bounds on the rate at which the distribution of fire can be changed. The structure of the optimal fire distribution policy is examined. It is shown that such command and control limitations do not essentially alter the optimal fire distribution decision rules, although the shifting of fires is initiated earlier when command and control limitations exist than when an entire force can instantaneously shift their fires from one target type to another. Thus, when there is inertia to overcome in shifting fires, one begins to change the distribution of fire before target priorities change in anticipation of this coming change. The theory of state variable inequality constraints plays a major role in solving this problem. Of particular mathematical difficulty is the presence of a second order state variable inequality constraint in the problem. (Author)