Control of a Discrete Dynamical System with Noise

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 speci...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 262; no. 6; pp. 869 - 877
Main Authors Ukhobotov, V. I., Nikitina, S. A.
Format Journal Article
LanguageEnglish
Published New York Springer US 16.04.2022
Springer
Springer Nature B.V
Subjects
Analysis
Control systems
Dynamical systems
Linear functions
Linearity
Mathematics
Mathematics and Statistics
Noise control
Polyhedra
multi-step control problem
93C55
discrete system
93C41
polyhedron of control values
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ISSN1072-3374
1573-8795
1573-8795
DOI10.1007/s10958-022-05866-0

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Summary: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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ISSN:1072-3374
1573-8795
1573-8795
DOI:10.1007/s10958-022-05866-0