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Avtomatika i Telemekhanika, 2017, Issue 10, Pages 139–154 (Mi at14617)  

This article is cited in 8 scientific papers (total in 8 papers)

Stochastic Systems

On the existence of optimal strategies in the control problem for a stochastic discrete time system with respect to the probability criterion

A. I. Kibzun, A. N. Ignatov

Moscow Aviation Institute, Moscow, Russia
Full-text PDF (651 kB) Citations (8)
References:
Abstract: We study a control problem for a stochastic system with discrete time. The optimality criterion is the probability of the event that the terminal state function does not exceed a given limit. To solve the problem, we use dynamic programming. The loss function is assumed to be lower semicontinuous with respect to the terminal state vector, and the transition function from the current state to the next is assumed to be continuous with respect to all its arguments. We establish that the dynamic programming algorithm lets one in this case find optimal positional control strategies that turn out to be measurable. As an example we consider a two-step problem of security portfolio construction. We establish that in this special case the future loss function on the second step turns out to be continuous everywhere except one point.
Keywords: dynamic programming, stochastic system, discrete time, measurable positional strategy.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 2.2461.2017/ПЧ
This work was done as part of fulfilling the state commission of the Ministry of Education and Science of the Russian Federation (state contracts no. 2.2461.2017/PCh).
Presented by the member of Editorial Board: B. M. Miller

Received: 16.12.2016
English version:
Automation and Remote Control, 2017, Volume 78, Issue 10, Pages 1845–1856
DOI: https://doi.org/10.1134/S0005117917100083
Bibliographic databases:
Document Type: Article
PACS: 02.50.Le
MSC: 93E20
Language: Russian
Citation: A. I. Kibzun, A. N. Ignatov, “On the existence of optimal strategies in the control problem for a stochastic discrete time system with respect to the probability criterion”, Avtomat. i Telemekh., 2017, no. 10, 139–154; Autom. Remote Control, 78:10 (2017), 1845–1856
Citation in format AMSBIB
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\by A.~I.~Kibzun, A.~N.~Ignatov
\paper On the existence of optimal strategies in the control problem for a~stochastic discrete time system with respect to the probability criterion
\jour Avtomat. i Telemekh.
\yr 2017
\issue 10
\pages 139--154
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\elib{https://elibrary.ru/item.asp?id=30067047}
\transl
\jour Autom. Remote Control
\yr 2017
\vol 78
\issue 10
\pages 1845--1856
\crossref{https://doi.org/10.1134/S0005117917100083}
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  • https://www.mathnet.ru/eng/at14617
  • https://www.mathnet.ru/eng/at/y2017/i10/p139
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Avtomatika i Telemekhanika
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    Full-text PDF :48
    References:37
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