Abstract:
A variant of the program iteration method called stability iterations is used for a differential game of pursuit–evasion. The successful solvability set of one of the problems generating the game is found as a limit of the iterative procedure in the space of sets whose elements are positions of the game. The game is defined by a pair of closed sets, one of the which is the target set in the pursuit problem (the first player's problem) and the other specifies the state constraints in this problem. For the positions not belonging to the solvability set of the pursuit problem, it is interesting to determine the smallest “size” of a neighborhood of the two mentioned sets for which the first player can implement the guidance to the neighborhood of the target set corresponding to this “size” within the similar neighborhood of the second set, i.e., the set specifying the state constraints. Similar constructions are considered for the sets realized at each stage of the iterative procedure. We use the connection of these constructions with the mentioned smallest “size” of neighborhoods of the sets that are parameters of the differential game in the sense of guaranteed realizability of guidance under the replacement of the original sets by these neighborhoods.
Keywords:
differential game of pursuit–evasion, program iteration method, guaranteed guidance.
Citation:
A. G. Chentsov, D. M. Khachai, “Relaxation of the Pursuit–Evasion Differential Game and Iterative Methods”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 4, 2018, 246–269; Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S35–S57
\Bibitem{CheKha18}
\by A.~G.~Chentsov, D.~M.~Khachai
\paper Relaxation of the Pursuit--Evasion Differential Game and Iterative Methods
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 4
\pages 246--269
\mathnet{http://mi.mathnet.ru/timm1591}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-4-246-269}
\elib{https://elibrary.ru/item.asp?id=36517715}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2020
\vol 308
\issue , suppl. 1
\pages S35--S57
\crossref{https://doi.org/10.1134/S0081543820020042}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000464575200020}
Linking options:
https://www.mathnet.ru/eng/timm1591
https://www.mathnet.ru/eng/timm/v24/i4/p246
This publication is cited in the following 7 articles:
A. G. Chentsov, “Guidance–Evasion Differential Game: Alternative Solvability and Relaxations of the Guidance Problem”, Proc. Steklov Inst. Math., 315 (2021), 270–289
A. G. Chentsov, “Differential approach-evasion game: alternative solvability and the construction of relaxations”, Differ. Equ., 57:8 (2021), 1088–1114
A. G. Chentsov, D. M. Khachai, “Operator programmnogo pogloscheniya i relaksatsiya differentsialnoi igry sblizheniya–ukloneniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:1 (2020), 64–91
A. G. Chentsov, “Nekotorye voprosy teorii differentsialnykh igr s fazovymi ogranicheniyami”, Izv. IMI UdGU, 56 (2020), 138–184
A. G. Chentsov, D. M. Khachay, “Relaxation of a dynamic game of guidance and program constructions of control”, Minimax Theory Appl., 5:2, SI (2020), 275–304
A. Chentsov, D. Khachay, “Towards a relaxation of the pursuit-evasion differential game”, IFAC PAPERSONLINE, 52:13 (2019), 2303–2307
Alexander Chentsov, Daniel Khachay, Studies in Systems, Decision and Control, 203, Advanced Control Techniques in Complex Engineering Systems: Theory and Applications, 2019, 129
Citation in format AMSBIB
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