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Avtomat. i Telemekh., 2018, Issue 2, Pages 3–18 (Mi at14721)  

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

Bilateral estimation of the Bellman function in the problems of optimal stochastic control of discrete systems by the probabilistic performance criterion

V. M. Azanov, Yu. S. Kan

Moscow Aviation Institute (National State University), Moscow, Russia

Abstract: Consideration was given to the optimal control of discrete stochastic systems by the probabilistic quality criterion. The new characteristics of the Bellman equation for this class of problems were examined, and the two-sided estimate of the Bellman function was determined. The problem of optimal control of the security portfolio with one riskless and a given number of risk assets was considered by way of example. The class of strategies featuring asymptotic optimality was established using the two-sided estimate of the Bellman function.

Keywords: optimal stochastic control, probabilistic criterion, discrete systems, dynamic programming method.

Funding Agency Grant Number
Russian Science Foundation 16-11-00062
Russian Foundation for Basic Research 15-08-02833
Results of Section 3 were supported by the Russian Foundation for Basic Research, project no. 15-08-02833. Other studies have been supported by the Russian Scientific Foundation, project no. 16-11-00062.

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English version:
Automation and Remote Control, 2018, 79:2, 203–215

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Presented by the member of Editorial Board: . . 

Received: 20.03.2017

Citation: V. M. Azanov, Yu. S. Kan, “Bilateral estimation of the Bellman function in the problems of optimal stochastic control of discrete systems by the probabilistic performance criterion”, Avtomat. i Telemekh., 2018, no. 2, 3–18; Autom. Remote Control, 79:2 (2018), 203–215

Citation in format AMSBIB
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\by V.~M.~Azanov, Yu.~S.~Kan
\paper Bilateral estimation of the Bellman function in the problems of optimal stochastic control of discrete systems by the probabilistic performance criterion
\jour Avtomat. i Telemekh.
\yr 2018
\issue 2
\pages 3--18
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\elib{http://elibrary.ru/item.asp?id=32606199}
\transl
\jour Autom. Remote Control
\yr 2018
\vol 79
\issue 2
\pages 203--215
\crossref{https://doi.org/10.1134/S0005117918020017}
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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. Bashkirtseva I., Pisarchik A.N., “Stochastic Analysis and Control in Kinetics of Multistable Chemical Reactor”, IFAC PAPERSONLINE, 51:32 (2018), 545–549  crossref  isi  scopus
    2. V. M. Azanov, Yu. S. Kan, “On optimal retention of the trajectory of discrete stochastic system in tube”, Autom. Remote Control, 80:1 (2019), 30–42  mathnet  crossref  crossref  isi  elib
    3. V. M. Azanov, Yu. S. Kan, “Usilennaya otsenka funktsii Bellmana v zadachakh stokhasticheskogo optimalnogo upravleniya s veroyatnostnym kriteriem kachestva”, Avtomat. i telemekh., 2019, no. 4, 53–69  mathnet  crossref  elib
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