Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/103177
Title: Some questions of differential game theory with phase constraints
Некоторые вопросы теории дифференциальных игр с фазовыми ограничениями
Authors: Chentsov, A. G.
Issue Date: 2020
Publisher: Udmurt State University
Citation: Chentsov A. G. Some questions of differential game theory with phase constraints / A. G. Chentsov. — DOI 10.35634/2226-3594-2020-56-10 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2020. — Vol. 56. — P. 138-184.
Abstract: Differential game (DG) of guidance-evasion is considered; moreover, its relaxations constructed with due account for priority considerations in the implementation of target set (TS) guidance and phase constraints (PC) validity are considered. We suppose that TS is closed in a natural topology of position space. With respect to the set that defines PC, it is postulated that the sections corresponding to time fixing are closed. For this setting, with the use of program iteration method (PIM), a variant of alternative for some natural (asymmetric) classes of strategies is established. A scheme of relaxation for the game guidance problem with nonclosed (in general case) set defining PC is considered. Under relaxation construction, reasons connected with priority in the implementation of guidance to TS and PC validity are taken into account (the case of asymmetric weakening of conditions of game ending is investigated). A position function is introduced, values of which (with priority correction) play the role of an analogue of least size for neighborhoods of TS and set defining PC under which it is possible to get a guaranteed solution of a relaxed problem of a player interested in approaching with TS while observing PC. It is demonstrated that the value of given function (when fixing the position of the game) is a price of DG for minimax–maximin quality functional which characterizes both the “degree” of approaching with TS and the “degree” of observance of initial PC. © 2020 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta.
Keywords: ALTERNATIVE
DIFFERENTIAL GAME
PROGRAM ITERATION METHOD
QUASISTRATEGY
RELAXATION OF APPROACH PROBLEM
URI: http://hdl.handle.net/10995/103177
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85099112046
PURE ID: 20249197
ISSN: 22263594
DOI: 10.35634/2226-3594-2020-56-10
metadata.dc.description.sponsorship: he study was funded by RFBR, project number 18–01–00410.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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