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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 4, Pages 489–501
DOI: https://doi.org/10.35634/vm220401 (Mi vuu822) 		 
MATHEMATICS

A mean field type differential inclusion with upper semicontinuous right-hand side

Y. V. Averboukhab

a Institute of Natural Sciences and Mathematics, Ural Federal University, ul. Turgeneva, 4, Yekaterinburg, 620000, Russia
b Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
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DOI: https://doi.org/10.35634/vm220401
Abstract: Mean field type differential inclusions appear within the theory of mean field type control through the convexification of a right-hand side. We study the case when the right-hand side of a differential inclusion depends on the state of an agent and the distribution of agents in an upper semicontinuous way. The main result of the paper is the existence and the stability of the solution of a mean field type differential inclusion. Furthermore, we show that the value function of the mean field type optimal control problem depends on an initial state and a parameter semicontinuously.
Keywords: mean field type differential inclusions, mean field type optimal control, stability analysis.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-874
The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2022-874).
Received: 22.09.2022
Accepted: 05.12.2022
Bibliographic databases:
Document Type: Article
UDC: 517.977.57
MSC: 93A16, 93C25, 34G20, 47J22, 49N60
Language: English
Citation: Y. V. Averboukh, “A mean field type differential inclusion with upper semicontinuous right-hand side”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:4 (2022), 489–501
Citation in format AMSBIB
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\paper A mean field type differential inclusion with upper semicontinuous right-hand side
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
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\vol 32
\issue 4
\pages 489--501
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\crossref{https://doi.org/10.35634/vm220401}
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    		Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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