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Russia Yekaterinburg
Section Mathematics
Title Positional strategies in mean-field 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 Sciencesa
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 finite-dimensional 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 mean-field control problems on a finite state space, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 15-21.
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