Application of differential games to problems of military conflict: Tactical allocation problems, Part II

Abstract

The mathematical theory of optimal control/differential games is used to study the structure of optimal allocation policies for some tactical allocation problems with combat described by Lanchester-type equations of warfare. Both deterministic and stochastic attrition processes are considered. For the optimal control of deterministic Lanchester-type attrition process, a general solution algorithm for the synthesis of the optimal policy is developed. Optimal allocation policies are developed for numerous one-sided optimization problems of tactical interest in order to study the dependence of the structure of these optimal policies on model form. Consideration has been given to singular extremals, multiple extremals (including dispersal surfaces), and state variable inequality constraints. It is shown how to apply the theory of state variable inequality constraints to determine the optimal control of deterministic Lanchester-type processes in order to treat non-negativity restrictions on force levels and thus to study the dependence of optimal policies upon the force levels. Various attrition models are considered (reflecting different assumptions as to target acquisition process, command and control capabilities, target engagement process, variations in range capabilities of weapon systems). Solutions are developed for Lanchester-type equations of modern warfare with variable attrition-rate coefficients. The optimal control of the Lanchester stochastic process is studied. (Author)