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Dynamic Games and Applications
Erschienen in: Dynamic Games and Applications 3/2017

03.06.2016

Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space

verfasst von: Idham Arif Alias, Gafurjan Ibragimov, Askar Rakhmanov

Erschienen in: Dynamic Games and Applications | Ausgabe 3/2017

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Abstract

We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space \(\ell _2\). Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is said to be possible. Problem is to find conditions of evasion. The main result of the paper is that if either (i) the total resource of evaders is greater than that of pursuers or (ii) the total resource of evaders is equal to that of pursuers and initial positions of all the evaders are not limit points for initial positions of the pursuers, then evasion is possible. Strategies for the evaders are constructed.
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Literatur
1.
Alexander S, Bishop R, Christ R (2009) Capture pursuit games on unbounded domain. Lënseignement Mathëmatique 55(1/2):103–125MathSciNetCrossRefMATH
2.
3.
Belousov AA (2010) Method of resolving functions for differential games with integral constraints. Theory Optim Solut 9:10–16 (in Russian)
4.
Blagodatskikh AI, Petrov NN (2009) Conflict interaction of groups of controlled objects. Udmurt State University, Izhevsk (in Russian)
5.
6.
7.
8.
Chikrii AA, Belousov AA (2010) On linear differential games with integral constraints. Proc Steklov Inst Math 269(Issue 1 Supplement):69–80MATH
9.
Chodun W (1988) Avoidance of many pursuers in differential games described by differential inclusions. J Math Anal Appl 135:581–590MathSciNetCrossRefMATH
10.
Gamkrelidze RV, Kharatashvili GL (1974) A differential game of evasion with nonlinear control. SIAM J Control 12(2):332–349MathSciNetCrossRef
11.
Grigorenko NL (1990) Mathematical methods of control for several dynamic processes. Izdat Gos Univ, Moscow (in Russian)
12.
Gusyatnikov PB (1978) A differential game of evasion. Kibernerika 4:72–77 (in Russian)
13.
Ibragimov GI, Azamov A, Khakestari M (2011) Solution of a linear pursuit–evasion game with integral constraints. Anziam J 52(E):E59–E75MathSciNetCrossRefMATH
14.
Ibragimov G, Salimi M, Amini M (2012) Evasion from many pursuers in simple motion differential game with integral constraints. Eur J Oper Res 218(2):505–511MathSciNetCrossRefMATH
15.
16.
Ibragimov GI, Allahabi F, Kuchkarov A (2014) A pursuit problem in an infinite system of second-order differential equations. Ukr Math J 65(8):1203–1216MathSciNetCrossRefMATH
17.
18.
Ibragimov G, Salleh Y (2012) Simple motion evasion differential game of many pursuers and one evader with integral constraints on control functions of players. J Appl Math. doi:10.​1155/​2012/​748096. Article ID 748096
19.
Ibragimov G, Satimov N (2012) A multiplayer pursuit differential game on a closed convex set with integral constraints. Abstr Appl Anal. doi:10.​1155/​2012/​460171. Article ID 460171
20.
Ivanov RP (1980) Simple pursuit–evasion on a compactum. Sov Math Dokl 22, 579–583 (translation from Dokl Akad Nauk SSSR 254(6):1318–1321 (1980))
21.
Krasovskii NN, Subbotin AI (1974) Positional differential games. Nauka, Moscow (in Russian)MATH
22.
23.
Mesencev AV (1974) Sufficient escape conditions for linear games with integral constraints. Doklady Akademii Nauk SSSR 218(5):1021–1023 (in Russian)MathSciNet
24.
Mishchenko EF, Nikol’skii MS, Satimov N (1980) The problem of avoiding encounter in \(n\)-person differential games. Proc Steklov Inst Math 143:111–136 (translation from Tr Mat Inst Steklova 143:105–128 (1977))
25.
Nikol’skii MS (1975) A quasilinear evasion problem. Sov Math Dokl 16:379–383 (translation from. Dokl Akad Nauk SSSR 221(2):539–542 (1975))
26.
Nikol’skii MS (1969) The direct method in linear differential games with integral constraints. Controll Syst IM, IK, SO AN SSSR 2:49–59 (in Russian)MathSciNet
27.
Petrosjan LA (1966) Pursuit games with many participants. Izv Akad Nauk Arm SSR 1(5):331–340 (in Russian)
28.
Petrov NN (1997) Simple pursuit of rigidly linked evaders. Autom Remote Control 58(12):1914–1919MathSciNetMATH
29.
Pontryagin LS, Mishchenko YF (1969) The problem of avoiding a controlled object by another object. Dokl Akad Nauk SSSR 189(4):721–723 (in Russian)MathSciNetMATH
30.
Pontryagin LS, Mishchenko EF (1971) The problem of evading the encounter in linear differential games. Differ Uravn 7:436–445 (in Russian)MATH
31.
32.
Pshenichnii BN, Chikrii AA, Rappoport JS (1981) An efficient method of solving differential games with many pursuers. Dokl Akad Nauk SSSR 256:530–535 (in Russian)MathSciNet
33.
Sakharov DV (2010) About one differential game of pursuit with many persons. Bull Udmurt Univ Math Mech Comput Sci 1:81–88 (in Russian)
34.
Salimi M, Ibragimov GI, Siegmund S, Sharifi S (2015) On a fixed duration pursuit differential game with geometric and integral constraints. Dyn Games Appl. doi:10.​1007/​s13235-015-0161-3
35.
Samatov BT (2013) Problems of group pursuit with integral constraints on controls of the players. I. Cybern Syst Anal 49(5):756–767MathSciNetCrossRefMATH
36.
37.
Satimov NY, Rikhsiev BB (2000) Methods of solving of evasion problems in mathematical control theory. Fan, Uzbekistan (in Russian)MATH
38.
Shiyuan J, Zhihua Q (2010) Pursuit–evasion games with multi-pursuer vs. one fast evader. In: Proceedings of the 8-th world congress on intelligent control and automation, pp 3184–3189
39.
Stipanovic DM, Melikyan AA, Hovakimyan N (2009) Some sufficient conditions for multi-player pursuit-evasion games with continuous and discrete observations. In: Bernhard P, Gaitsgory V, Pourtallier O (eds) Annals of the international society of dynamics games, Advances in dynamic games and applications, vol 10. Springer, Berlin, pp 133–145
40.
Subbotin AI, Ushakov VN (1975) Alternative for an encounter–evasion differential game with integral constraints on the players’ controls. J Appl Math Mech 39(3):387–396MathSciNetCrossRefMATH
41.
Ushakov VN (1972) Extremal strategies in differential games with integral constraints. PMM 36(1):15–23MathSciNetMATH
42.
Vagin DA, Petrov NN (2001) Simple pursuit of rigidly connected evaders. Izv Ross Akad Nauk TSU 5:75–79 (in Russian)MATH
Metadaten
Titel
Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space
verfasst von
Idham Arif Alias
Gafurjan Ibragimov
Askar Rakhmanov
Publikationsdatum
03.06.2016
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 3/2017
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-016-0196-0

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