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Russia Yekaterinburg
Section  Mathematics 
Title  Positional strategies in meanfield control problems on a finite state space 
Author(s)  Berezin A.A.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  We consider an optimal control problem for an infinite amount of agents of the same type. We assume that agents have a finite state space. The given formulation of the problem involves an objective functional that is common for all agents and a common control center that chooses a strategy for agents. A chosen strategy is supposed to be positional. In this paper we consider a case when the dynamics of agents is given by a Markov chain with continuous time. It is assumed that the Kolmogorov matrix of this chain in each state depends on the current state, the chosen control and the distribution of all agents. For the original problem, it is shown that concerning positional strategies the solution can be obtained through the solution of the deterministic control problem in a finitedimensional phase space. 
Keywords  markov chain, control problem, mean field 
UDC  517.977.5 
MSC  49J21, 60J28 
DOI  10.20537/vm180102 
Received  12 February 2018 
Language  Russian 
Citation  Berezin A.A. Positional strategies in meanfield control problems on a finite state space, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 1521. 
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