On a problem of reserves control in the presence of an interference

An approach is proposed to solving the problem of reserves control in the discrete case. A controlled process whose duration is known is considered. The problem of retaining a phase point in a given family of sets at discrete time instants is solved. The case is considered when the control vectogram and the given family of sets are polyhedra defined using the system of linear inequalities. It is assumed that a certain linearity property is fulfilled for polyhedrals. An algorithm for constructing a control is written, which ensures the retention of the phase point in a given family of sets for any permissible implementation of the interference. In the practical part of the work, the application of the obtained results is shown by an example.