Geodesic
On two differential games of simple group pursuit
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 50-59 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Two differential games of the simple pursuit of a group of evaders by a group of pursuers are considered. The first problem is devoted to the pursuit of a group of rigidly co-ordinated evaders by a group of pursuers with equal possibilities for all participants. It is supposed that the evaders remain in the bounds of the convex polyhedral set, terminal sets are convex compacts and the aim of the group of pursuers is to capture at least one evader. The solvability conditions of the problem of pursuit and the problem of evasion are obtained in the terms of initial positions and parameters of the game. The second problem is devoted to the pursuit of a group of evaders by a group of pursuers under condition that the evaders use program strategies and one pursuer can catch only one evader. The aim of a group of pursuers is to capture a specified number of evaders. Terminal sets are convex compacts, the set of possible controls is an arbitrary convex compact. Necessary and sufficient solvability conditions of the problem of pursuit are obtained.
Keywords: differential game, group pursuit, rigidly co-ordinated evaders.
Mots-clés : simple motion 
@article{VUU_2012_1_a5,
     author = {D. V. Sakharov},
     title = {On two differential games of simple group pursuit},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {50--59},
     year = {2012},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2012_1_a5/}
}
TY  - JOUR
AU  - D. V. Sakharov
TI  - On two differential games of simple group pursuit
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2012
SP  - 50
EP  - 59
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VUU_2012_1_a5/
LA  - ru
ID  - VUU_2012_1_a5
ER  - 
%0 Journal Article
%A D. V. Sakharov
%T On two differential games of simple group pursuit
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2012
%P 50-59
%N 1
%U http://geodesic.mathdoc.fr/item/VUU_2012_1_a5/
%G ru
%F VUU_2012_1_a5
D. V. Sakharov. On two differential games of simple group pursuit. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 50-59. http://geodesic.mathdoc.fr/item/VUU_2012_1_a5/

[1] Petrosyan L. A., “Igry presledovaniya so mnogimi uchastnikami”, Izvestiya AN Arm. SSR, 1:5 (1966), 331–340 | MR

[2] Pshenichnyi B. N., “Prostoe presledovanie neskolkimi ob'ektami”, Kibernetika, 1976, no. 3, 145–146

[3] Ivanov R. P., “Prostoe presledovanie na kompakte”, DAN SSSR, 254:6 (1978), 1318–1321 | MR

[4] Chikrii A. A., Konfliktno upravlyaemye protsessy, Nauk. dumka, Kiev, 1992, 240 pp.

[5] Grigorenko N. L., Matematicheskie metody upravleniya neskolkimi dinamicheskimi protsessami, Izd-vo Mosk. un-ta, M., 1990, 197 pp.

[6] Blagodatskikh A. I., Petrov N. N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov, Izd-vo “Udmurtskii universitet”, Izhevsk, 2009, 266 pp. | MR | Zbl

[7] Petrov N. N., Petrov N. Nikandr., “O differentsialnoi igre ‘kazaki-razboiniki’ ”, Differentsialnye uravneniya, 19:8 (1983), 1366–1374 | MR | Zbl

[8] Bannikov A. S., “Ob odnoi zadache prostogo presledovaniya”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 3, 3–11 | MR

[9] Bannikov A. S., Petrov N. N., “K nestatsionarnoi zadache gruppovogo presledovaniya s fazovymi ogranicheniyami”, Trudy Instituta matematiki i mekhaniki UrO RAN, 16, no. 1, 2010, 40–51

[10] Sakharov D. V., “Ob odnoi differentsialnoi igre presledovaniya so mnogimi uchastnikami”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 1, 81–88

[11] Vagin D. A., Petrov N. N., “Zadacha presledovaniya gruppy zhestko skoordinirovannykh ubegayuschikh”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2001, no. 5, 75–79 | MR | Zbl

[12] Petrov N. N., Prokopenko V. A., “Ob odnoi zadache presledovaniya gruppy ubegayuschikh”, Differentsialnye uravneniya, 23:4 (1987), 724–726 | MR