Abstract
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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 168, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part I, 2019.
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Ukhobotov, V.I., Nikitina, S.A. Control of a Discrete Dynamical System with Noise. J Math Sci 262, 869–877 (2022). https://doi.org/10.1007/s10958-022-05866-0
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DOI: https://doi.org/10.1007/s10958-022-05866-0