Model of Lanchester as discrete control system

We consider the discrete analogue Lanchester model describing the behavior of the two opposing members of the military conflict. The main characteristic of the number of parties are rivals, varying depending on various factors, such as caused by the actions of competitors, and not directly related to military operations. The target is to achieve the desired number of armies at the end of a given period. The solution of the proposed task is reduced to finding the optimal control action in the corresponding linear discrete control system.