|
Section
|
Mathematics
|
|
Title
|
To the problem of Chernous'ko
|
|
Author(-s)
|
Petrov N.N.a,
Shchelchkov K.A.a
|
|
Affiliations
|
Udmurt State Universitya
|
|
Abstract
|
The problem of simple pursuit of one evader by the group of pursuers is studied, provided that among the pursuers there are both members, the maximum speeds of which coincide with the maximum speed of the evader, and participants whose maximum speeds are strictly less than the maximum speed of the evader, while the evader does not leave a convex polyhedral set. The conditions under which the pursuers with fewer capabilities do not affect the solvability of problem of evasion are obtained.
|
|
Keywords
|
differential game, simple motion, group pursuit, phase restrictions
|
|
UDC
|
517.977
|
|
MSC
|
49N70, 49N75
|
|
DOI
|
10.20537/vm120405
|
|
Received
|
29 August 2012
|
|
Language
|
Russian
|
|
Citation
|
Petrov N.N., Shchelchkov K.A. To the problem of Chernous'ko, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 4, pp. 62-67.
|
|
References
|
- Chernous’ko F.L. One problem of evasion from many pursuers, Prikl. Mat. Mekh., 1976, vol. 40, no. 1, pp. 14–24.
- Pshenichnyi B.N. Simple pursuit by a few objects, Kibernetika, 1976, no. 3, pp. 145–146.
- Grigorenko N.L. Simple pursuit–evasion game of pursuit group and one evader, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 1983, no. 1, pp. 41–47.
- Ivanov R.P. Simple pursuit in a compact set, Doklady Akademii Nauk SSSR, 1978, vol. 254, no. 6, pp. 1318–1321.
- Petrov N.N. The simple pursuit with phase constraints, Leningrad State University, Leningrad, 1984, 16 p. Deposited in VINITI 27.03.1984., no. 1684-84.
- Petrov N.N. A certain simple pursuit problem with phase constraints, Automation and Remote Control, 1992, vol. 53, no. 5, pp. 639–642.
- Bannikov A.S. On one problem of simple pursuit, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, no. 3, pp. 3–11.
- Bannikov A.S., Petrov N.N. On non-stationary problem group pursuit with phase restrictions, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2010, vol. 16, no. 1, pp. 40–51.
- Petrov N.N. On the nonstationary problem of group pursuit with phase constraints, Mat. Teor. Igr Prilozh., 2010, vol. 2, no. 4, pp. 74–83.
- Petrov N.N. About one problem of group pursuit with phase constraints, Prikl. Mat. Mekh., 1988, vol. 52, no. 6, pp. 1060–1063.
- Petrov N.N. One linear problem of evasion from many pursuers, Izv. Ross. Akad. Nauk, Teor. Sist. Upravl., 1988, no. 1, pp. 41–43.
- Shuravina I.N. About the one problem of evasion in cone, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, no. 2, pp. 13–16.
- Sakharov D.V. On two differential games of simple group pursuit, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, no. 1, pp. 50–59.
- Zhimovsky V. Two results of solving one problem of evasion from many pursuers, Bull. Pol. Acad. Sci., Math., 1980, vol. 28, no. 3–4, pp. 155–159
|
|
Full text
|
|
+7 (3412) 91 60 92
Russian