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 Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 3, Pages 292–302 (Mi timm1220)

A control problem under incomplete information for a linear stochastic differential equation

V. L. Rozenberg

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

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 open-loop 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.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, 295, suppl. 1, 145–155

Bibliographic databases:

Document Type: Article
UDC: 517.977.1

Citation: V. L. Rozenberg, “A control problem under incomplete information for a linear stochastic differential equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 3, 2015, 292–302; Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 145–155

Citation in format AMSBIB
\Bibitem{Roz15} \by V.~L.~Rozenberg \paper A control problem under incomplete information for a linear stochastic differential equation \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2015 \vol 21 \issue 3 \pages 292--302 \mathnet{http://mi.mathnet.ru/timm1220} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468111} \elib{http://elibrary.ru/item.asp?id=24156733} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2016 \vol 295 \issue , suppl. 1 \pages 145--155 \crossref{https://doi.org/10.1134/S0081543816090157} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. P. G. Surkov, “The problem of closed-loop guidance by a given time for a linear control system with delay”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 218–227
2. V. I. Maksimov, P. G. Surkov, “O razreshimosti zadachi garantirovannogo paketnogo navedeniya na sistemu tselevykh mnozhestv”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 344–354
3. Surkov Platon Gennad'evich, “The Problem of Package Guidance Under Incomplete Information and Integral Signal of Observation”, Sib. Electron. Math. Rep., 15 (2018), 373–388
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