Avtomatika i Telemekhanika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Avtomat. i Telemekh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Avtomatika i Telemekhanika, 2020, Issue 10, Pages 93–117
DOI: https://doi.org/10.31857/S0005231020100037
(Mi at15406)
 

This article is cited in 2 scientific papers (total in 2 papers)

Stochastic Systems

Probabilistic criterion-based optimal retention of trajectories of a discrete-time stochastic system in a given tube: bilateral estimation of the Bellman function

V. M. Azanov, A. N. Tarasov

Moscow Aviation Institute (National Research University), Moscow, Russia
Full-text PDF (586 kB) Citations (2)
References:
Abstract: This paper examines an optimal control problem with a probabilistic criterion for retaining the trajectories of a discrete-time stochastic system in given sets. The dynamic programming method is employed for obtaining the isobells of levels 1 and 0 of the Bellman function, two-sided estimates for the right-hand side of the dynamic programming equation, two-sided estimates for the Bellman function, and the optimal-value function of the probabilistic criterion. These results are then used for deriving an approximate formula for the optimal control. As an illustrative example the problem of keeping an inverted pendulum in the neighborhood of an unstable equilibrium is considered.
Keywords: discrete-time systems, stochastic optimal control, probabilistic criterion, dynamic programming, Bellman function, inverted pendulum.
Funding agency Grant number
Russian Science Foundation 16-11-00062
Russian Foundation for Basic Research 18-08-00595_а
This work, with the exception of Section 4, was supported by the Russian Science Foundation, project no. 16-11-00062. The results of Section 4 were established under support of the Russian Foundation for Basic Research, project no. 18-08-00595.
Presented by the member of Editorial Board: A. V. Nazin

Received: 24.12.2019
Revised: 20.05.2020
Accepted: 09.07.2020
English version:
Automation and Remote Control, 2020, Volume 81, Issue 10, Pages 1819–1839
DOI: https://doi.org/10.1134/S0005117920100033
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Azanov, A. N. Tarasov, “Probabilistic criterion-based optimal retention of trajectories of a discrete-time stochastic system in a given tube: bilateral estimation of the Bellman function”, Avtomat. i Telemekh., 2020, no. 10, 93–117; Autom. Remote Control, 81:10 (2020), 1819–1839
Citation in format AMSBIB
\Bibitem{AzaTar20}
\by V.~M.~Azanov, A.~N.~Tarasov
\paper Probabilistic criterion-based optimal retention of trajectories of a discrete-time stochastic system in a given tube: bilateral estimation of the Bellman function
\jour Avtomat. i Telemekh.
\yr 2020
\issue 10
\pages 93--117
\mathnet{http://mi.mathnet.ru/at15406}
\crossref{https://doi.org/10.31857/S0005231020100037}
\elib{https://elibrary.ru/item.asp?id=45143146}
\transl
\jour Autom. Remote Control
\yr 2020
\vol 81
\issue 10
\pages 1819--1839
\crossref{https://doi.org/10.1134/S0005117920100033}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000590544900003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85096226891}
Linking options:
  • https://www.mathnet.ru/eng/at15406
  • https://www.mathnet.ru/eng/at/y2020/i10/p93
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Avtomatika i Telemekhanika
    Statistics & downloads:
    Abstract page:176
    Full-text PDF :31
    References:28
    First page:16
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024