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Avtomatika i Telemekhanika, 2007, Issue 6, Pages 99–115 (Mi at1004)  

This article is cited in 1 scientific paper (total in 1 paper)

Stochastic Systems

Local solutions of the Hamilton–Jacobi–Bellman equation for some stochastic problems

A. S. Bratus'a, A. P. Ivanovaa, J. Menaldib, D. V. Yurchenkoa

a Moscow State University of Railway Communications
b Wayne State University, Detroit
Full-text PDF (288 kB) Citations (1)
References:
Abstract: Consideration is given to the control problem of motion of a linear oscillator, which is subject to the external Gaussian and Poisson random actions, with the aim to minimize the mean energy with the aid of the external bounded control force. The hybrid solution method is suggested for the solution of the stated problem. This method relies on the search in a portion of the phase space for the exact analytical solution of the appropriate Hamilton–Jacobi–Bellman (HJB) equation and the numerical solution of this equation in the remaining (bounded) portion of the space. It is proved that the found analytical solutions represent the asymptotics of solutions of the Hamilton–Jacobi–Bellman equation. With the aid of the decomposition method, the obtained results are applied to the problem for the suppression with the aid of the actuator of vibrations of an elastic rod (plate) that is found to be under the action of Gaussian random actions. Results of the numerical modeling are given.
Presented by the member of Editorial Board: B. M. Miller

Received: 22.12.2005
English version:
Automation and Remote Control, 2007, Volume 68, Issue 6, Pages 1023–1038
DOI: https://doi.org/10.1134/S0005117907060094
Bibliographic databases:
Document Type: Article
PACS: 02.30.Yy, 45.30.+s, 02.50.Fz
Language: Russian
Citation: A. S. Bratus', A. P. Ivanova, J. Menaldi, D. V. Yurchenko, “Local solutions of the Hamilton–Jacobi–Bellman equation for some stochastic problems”, Avtomat. i Telemekh., 2007, no. 6, 99–115; Autom. Remote Control, 68:6 (2007), 1023–1038
Citation in format AMSBIB
\Bibitem{BraIvaMen07}
\by A.~S.~Bratus', A.~P.~Ivanova, J.~Menaldi, D.~V.~Yurchenko
\paper Local solutions of the Hamilton--Jacobi--Bellman equation for some stochastic problems
\jour Avtomat. i Telemekh.
\yr 2007
\issue 6
\pages 99--115
\mathnet{http://mi.mathnet.ru/at1004}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2352082}
\zmath{https://zbmath.org/?q=an:1142.93038}
\transl
\jour Autom. Remote Control
\yr 2007
\vol 68
\issue 6
\pages 1023--1038
\crossref{https://doi.org/10.1134/S0005117907060094}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547317882}
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  • https://www.mathnet.ru/eng/at1004
  • https://www.mathnet.ru/eng/at/y2007/i6/p99
  • This publication is cited in the following 1 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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    Abstract page:394
    Full-text PDF :136
    References:63
    First page:1
     
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