Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2018, Volume 14, Issue 4, Pages 302–315
DOI: https://doi.org/10.21638/11701/spbu10.2018.403
(Mi vspui378)
 

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

Applied mathematics

A method for solving differential inclusions with fixed right end

A. V. Fominykh

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (417 kB) Citations (2)
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Abstract: In the paper, we study a differential inclusion with a given continuous convex multivalued mapping. For a given finite time interval, it is required to construct a solution of the differential inclusion, that satisfies the given initial condition or both the initial and final conditions. With the help of support functions, the original problem is reduced to the problem of global minimization of some functions in the space of piecewise continuous functions. In the case of continuous differentiability of the support function of a multivalued mapping with respect to the phase variables, this functional is Gateaux differentiable. In the paper, Gateaux gradient is found, necessary and (in some particular cases) sufficient conditions for the global minimum of the given functions are obtained. On the basis of these conditions, the method of steepest descent is applied to the original problem. Numerical examples illustrate the method realization.
Keywords: differential inclusions, support function, the steepest descent method.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00014 mol-a
The work is supported by Russian Found of Fundamental Research (project N 18-31-00014 mol-a).
Received: April 8, 2018
Accepted: September 25, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.977.58
MSC: 49M05
Language: English
Citation: A. V. Fominykh, “A method for solving differential inclusions with fixed right end”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 14:4 (2018), 302–315
Citation in format AMSBIB
\Bibitem{Fom18}
\by A.~V.~Fominykh
\paper A method for solving differential inclusions with fixed right end
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2018
\vol 14
\issue 4
\pages 302--315
\mathnet{http://mi.mathnet.ru/vspui378}
\crossref{https://doi.org/10.21638/11701/spbu10.2018.403}
\elib{https://elibrary.ru/item.asp?id=36687358}
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  • 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
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