Survey on the optimal control of Lanchester-type attrition processes

This is a survey paper on the author's research on applications of the mathematical theory of optimal control/differential games to problems of military conflict in order to study the structure of optimal tactical allocation policies. This program has been carried out for tactical allocation problems with the combat described by Lanchester-type equations of warfare. Both deterministic and stochastic attrition processes have been considered, although the major emphasis has been on the former. Optimal allocation policies have been developed for numerous one-sided optimization problems of tactical interest with deterministic Lanchester-type attrition processes in order to study the dependence of the structure of these optimal policies upon model form. Problem areas in applying current mathematical theories to solve such problems are discussed. An important gap in the existing theory of differential games is identified. 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). (Author)