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Russia Yekaterinburg
Year
2022
Volume
32
Issue
4
Pages
489-501
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Section Mathematics
Title A mean field type differential inclusion with upper semicontinuous right-hand side
Author(-s) Averboukh Yu.V.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
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
UDC 517.977.57
MSC 93A16, 93C25, 34G20, 47J22, 49N60
DOI 10.35634/vm220401
Received 22 September 2022
Language English
Citation Averboukh Yu.V. A mean field type differential inclusion with upper semicontinuous right-hand side, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 4, pp. 489-501.
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