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Ural Mathematical Journal, 2015, Volume 1, Issue 1, Pages 68–82
DOI: https://doi.org/10.15826/umj.2015.1.007
(Mi umj7)
 

This article is cited in 3 scientific papers (total in 3 papers)

A guaranteed control problem for a linear stochastic differential equation

Valeriy L. Rozenberg

N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
Full-text PDF (224 kB) Citations (3)
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Abstract: A problem of guaranteed closed-loop control under incomplete information is considered for a linear stochastic differential equation (SDE) from the viewpoint of the method of open-loop control packages worked out earlier for the guidance of a linear control system of ordinary differential equations (ODEs) to a convex target set. The problem consists in designing a deterministic control providing (irrespective of a realized initial state from a given finite set) prescribed properties of the solution (being a random process) at a terminal point in time. It is assumed that a linear signal on some number of realizations is observed. By the equations of the method of moments, the problem for the SDE is reduced to an equivalent problem for systems of ODEs describing the mathematical expectation and covariance matrix of the original process. Solvability conditions for the problems in question are written.
Keywords: Guidance problem, Guaranteed closed-loop control, Linear stochastic differential equation.
Funding agency Grant number
Russian Science Foundation 14-11-00539
This work was supported by the Russian Science Foundation (project no. 14-11-00539).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Valeriy L. Rozenberg, “A guaranteed control problem for a linear stochastic differential equation”, Ural Math. J., 1:1 (2015), 68–82
Citation in format AMSBIB
\Bibitem{Roz15}
\by Valeriy~L.~Rozenberg
\paper A guaranteed control problem for a linear stochastic differential equation
\jour Ural Math. J.
\yr 2015
\vol 1
\issue 1
\pages 68--82
\mathnet{http://mi.mathnet.ru/umj7}
\crossref{https://doi.org/10.15826/umj.2015.1.007}
\zmath{https://zbmath.org/?q=an:1396.93064}
\elib{https://elibrary.ru/item.asp?id=25613597}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Ural Mathematical Journal
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