Determitation of optimal allocation strategies for heterogeneous two-on-two differential combat

Abstract

This thesis is concerned with an optimal determination of force allocation strategies for a generalized two-on-two combat model of a heterogeneous, deterministic, constant attrition-rates, Lanchester-type process. Semi-heterogeneous models by Isbell and Marlow, and by Taylor, and the supporting fire distribution model by Weiss are extended to a generalized two-on-two combat model in which any component in one side may engage with any component of the opponent. Determination of optimal allocation strategies via theory of differential game is limited to specific situations because of the computational difficulties involved. Therefore, a new method for obtaining the desired accuracy and reducing high-speed memory requirements is developed using the analytic solutions and the state increment dynamic programming technique. For this purpose, analytic solutions to the two-on-two combat differential equations are obtained, dynamic programming model is established, and the existence and uniqueness of solution to multi-stage game are shown. Local error bound of interpolation is estimated and it is shown that this error converges to zero as the time interval and state increments approach to zero. Examples are given which demonstrate the superiority of this model over the previous results of Isbell and Marlow, Taylor, and Weiss.