Geodesic
Game pursuit problem with two pursuers and one evader: dependence of solution on parameters
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 32-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

A model linear differential game with two pursuers and one evader is considered. Results of numerical study of structure of level sets of the value function for different variants of the game parameters are given.
Keywords: multiple person pursuit-evasion games, linear dynamics, value function. 
@article{IIMI_2012_39_1_a13,
     author = {S. A. Ganebnyi and S. S. Kumkov and S. Le M\'enec and V. S. Patsko},
     title = {Game pursuit problem with two pursuers and one evader: dependence of solution on parameters},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {32--37},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a13/}
}
TY  - JOUR
AU  - S. A. Ganebnyi
AU  - S. S. Kumkov
AU  - S. Le Ménec
AU  - V. S. Patsko
TI  - Game pursuit problem with two pursuers and one evader: dependence of solution on parameters
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2012
SP  - 32
EP  - 37
VL  - 39
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a13/
LA  - ru
ID  - IIMI_2012_39_1_a13
ER  - 
%0 Journal Article
%A S. A. Ganebnyi
%A S. S. Kumkov
%A S. Le Ménec
%A V. S. Patsko
%T Game pursuit problem with two pursuers and one evader: dependence of solution on parameters
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2012
%P 32-37
%V 39
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a13/
%G ru
%F IIMI_2012_39_1_a13
S. A. Ganebnyi; S. S. Kumkov; S. Le Ménec; V. S. Patsko. Game pursuit problem with two pursuers and one evader: dependence of solution on parameters. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 32-37. http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a13/

[1] Shinar J., Shima T., “Non-orthodox Guidance Law Development Approach for Intercepting Maneuvering Targets”, Journal of Guidance, Control, and Dynamics, 25:4 (2002), 658–666 | DOI

[2] Le Ménec S., “Linear differential game with two pursuers and one evader”, Advances in Dynamic Games. Theory, Applications, and Numerical Methods for Differential and Stochastic Games, Annals of the International Society of Dynamic Games, 11, eds. M. Breton and K. Szajowski, Birkhauser, Boston, 2011, 209–226 | MR | Zbl

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

[4] Petrosyan L.A., Differentsialnye igry presledovaniya, Izd-vo Leningr. un-ta, Leningrad, 1977, 222 pp.

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

[6] Chikrii A.A., Konfliktno upravlyaemye protsessy, Naukova Dumka, Kiev, 1992, 384 pp.

[7] Blagodatskikh A.I., Petrov N.N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov, Udmurtskii un-t, Izhevsk, 2009, 266 pp.

[8] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp.

[9] Krasovskii N.N., Krasovskii A.N., “A differential game for the minimax of a positional functional”, Adv. Nonlin. Dynamics. and Control, A report from Russia, Birkhauser, Berlin, 1993, 41–73 | DOI | MR | Zbl