Problem of group pursuit in a Pontriagin's example
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 125-131 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A pursuit problem of one evader by a group of pursuers in stationary L. S. Pontriagin's example with equal possibilities for all participants is considered. It is supposed that the roots of the characteristic equation are simple and purely imaginary, the terminal sets are the convex compacts and the set of possible controls is arbitrary convex compact. The sufficient solvability conditions of the problem of pursuit are obtained, illustrative examples are presented.
Keywords: differential game, group pursuit, Pontriagin's example.
@article{VUU_2013_4_a11,
     author = {D. V. Sakharov},
     title = {Problem of group pursuit in {a~Pontriagin's} example},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {125--131},
     year = {2013},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_4_a11/}
}
TY  - JOUR
AU  - D. V. Sakharov
TI  - Problem of group pursuit in a Pontriagin's example
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2013
SP  - 125
EP  - 131
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2013_4_a11/
LA  - ru
ID  - VUU_2013_4_a11
ER  - 
%0 Journal Article
%A D. V. Sakharov
%T Problem of group pursuit in a Pontriagin's example
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2013
%P 125-131
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2013_4_a11/
%G ru
%F VUU_2013_4_a11
D. V. Sakharov. Problem of group pursuit in a Pontriagin's example. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 125-131. http://geodesic.mathdoc.fr/item/VUU_2013_4_a11/

[1] Petrosyan L. A., “Games of pursuit with many participants”, Izvestiya Akademii Nauk Arm. SSR, 1:5 (1966), 331–340 | MR

[2] Pshenichnyi B. N., “Simple pursuit by a few objects”, Kibernetika, 1976, no. 3, 145–146

[3] Chikrii A. A., Conflict controlled processes, Naukova Dumka, Kiev, 1992, 240 pp.

[4] Grigorenko N. L., Mathematical methods of control a few dynamic processes, Moscow State University, Moscow, 1990, 197 pp.

[5] Blagodatskikh A. I., Petrov N. N., Conflict interaction of groups of controlled objects, Udmurt State University, Izhevsk, 2009, 266 pp. | MR | Zbl

[6] Ganebny S. A., Kumkov S. S., Menec S. L., Patsko V. S., “Model problem in a line with two pursuers and one evader”, Dyn. Games Appl., 2:2 (2012), 228–257 | DOI | MR | Zbl

[7] Blagodatskikh A. I., “On an oscillatory conflict-controlled process with many players”, J. Comput. Syst. Sci., 2005, no. 2, 198–200 | MR | Zbl

[8] Blagodatskikh A. I., “On two oscillatory conflictly controlled processes with many persons”, Izv. Inst. Mat. Inform. Udmurt. Gos. Univ., 2005, no. 2, 3–22

[9] Blagodatskikh A. I., “Group pursuit in Pontryagin's nonstationary example”, Differential Equations, 44:1 (2008), 40–46 | DOI | MR | Zbl

[10] Petrov N. N., “Non-stationary Pontriagin's example with phase restrictions”, Problemy Upravleniya i Informatiki, 2000, no. 4, 18–24 | MR

[11] Bannikov A. S., Petrov N. N., “On a nonstationary problem of group pursuit”, Proceedings of the Steklov Institute of Mathematics, 271, 2010, 41–52 | DOI | Zbl

[12] Petrov N. N., “Multiple capture in Pontryagin's example with phase constraints”, J. Appl. Math. Mech., 61:5 (1997), 725–732 | DOI | MR | Zbl

[13] Sakharov D. V., “About one differential game of pursuit with many persons”, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2010, no. 1, 81–88

[14] Petrov N. N., “ ‘Soft’ capture in the L. S. Pontryagin example of many players”, J. Appl. Math. Mech., 67:5 (2003), 671–680 | DOI | MR | Zbl

[15] Bannikov A. S., “On one problem of simple pursuit”, Vestn. Udmurt. Univ., Mat. Mekh. Komp'yut. Nauki, 2009, no. 3, 3–11