Geodesic
A mean field type differential inclusion with upper semicontinuous right-hand side
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 4, pp. 489-501

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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. 
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     title = {A mean field type differential inclusion with upper semicontinuous right-hand side},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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Y. V. Averboukh. A mean field type differential inclusion with upper semicontinuous right-hand side. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 4, pp. 489-501. http://geodesic.mathdoc.fr/item/VUU_2022_32_4_a0/