Control of a Discrete Dynamical System with Noise - Ukhobotov, V. I.; Nikitina, S. A. (Journal of mathematical sciences (New York, N.Y.), 2022)
For a discrete dynamical control system with noise, we consider the problem of retaining a phase point in a given family of sets at discrete instants of time. We analyze the case where the control vectogram is a polyhedron defined by a system of linear inequalities. We prove some properties of specific polyhedra satisfying the linearity condition, which allows us to obtain a condition of retention in the explicit form. Necessary and sufficient conditions for the possibility of retention are given. The results obtained are illustrated by an example.