On a control problem for a discrete system

The article proposes one of the approaches for solving the control problem of a linear discrete system. A conflict-controlled process is considered whose duration is given. It is required that at the end of the control process the phase point is contained in a given set. Rules governing the control of a discrete system contain discrimination for the second player. The case is considered when the control vector and a given set are polyhedra given by a system of linear inequalities. It is assumed that for polyhedra a certain property of linearity is satisfied, which makes it possible to obtain the solution of the problem explicitly. The operator of operator absorption is introduced into the consideration in the paper. With the help of this operator, conditions are written for a set of initial positions under which the required inclusion is guaranteed at the time of the end of the control process. These conditions are written in the form of a system of inequalities. The practical part of the work shows the application of the obtained results to economic systems. The solution of the problem of inventory management is given.