Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111604
Title: Approximation of Value Function of Differential Game with Minimal Cost
Other Titles: Аппроксимация функции цены дифференциальной игры с критерием, задаваемым условием минимизации
Authors: Averboukh, Y. V.
Issue Date: 2021
Publisher: Udmurt State University
Udmurt State University
Citation: Averboukh Y. V. Approximation of Value Function of Differential Game with Minimal Cost [Аппроксимация функции цены дифференциальной игры с критерием, задаваемым условием минимизации] / Y. V. Averboukh // Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki. — 2021. — Vol. 31. — Iss. 4. — P. 536-561.
Abstract: The paper is concerned with the approximation of the value function of the zero-sum differential game with the minimal cost, i. e., the differential game with the payoff functional determined by the minimization of some quantity along the trajectory by the solutions of continuous-time stochastic games with the stopping governed by one player. Notice that the value function of the auxiliary continuous-time stochastic game is described by the Isaacs-Bellman equation with additional inequality constraints. The Isaacs-Bellman equation is a parabolic PDE for the case of stochastic differential game and it takes a form of system of ODEs for the case of continuous-time Markov game. The approximation developed in the paper is based on the concept of the stochastic guide first proposed by Krasovskii and Kotelnikova. © Yu. V. Averboukh.
Keywords: APPROXIMATION OF THE VALUE FUNCTION
DIFFERENTIAL GAMES WITH MINIMAL COST
ISAACS-BELLMAN EQUATION
STOCHASTIC GUIDE
URI: http://hdl.handle.net/10995/111604
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85123220368
PURE ID: 29308682
ISSN: 1994-9197
metadata.dc.description.sponsorship: This work was funded by the Russian Science Foundation (project no. 17-11-01093).
RSCF project card: 17-11-01093
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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