Geodesic
On a nonstationary problem of group pursuit
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 40-51

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Pontryagin's classical nonstationary example with many participants and phase constraints on the evader's states with equal dynamic and inertia capabilities of the players is considered. The case of a simple motion is considered separately. Solvability conditions for problems of pursuit and evasion are obtained.
Keywords: group pursuit, nonstationary problem, Pontryagin's example, phase constraints. 
A. S. Bannikov; N. N. Petrov. On a nonstationary problem of group pursuit. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 40-51. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a3/
@article{TIMM_2010_16_1_a3,
     author = {A. S. Bannikov and N. N. Petrov},
     title = {On a~nonstationary problem of group pursuit},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {40--51},
     year = {2010},
     volume = {16},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a3/}
}
TY  - JOUR
AU  - A. S. Bannikov
AU  - N. N. Petrov
TI  - On a nonstationary problem of group pursuit
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2010
SP  - 40
EP  - 51
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a3/
LA  - ru
ID  - TIMM_2010_16_1_a3
ER  - 
%0 Journal Article
%A A. S. Bannikov
%A N. N. Petrov
%T On a nonstationary problem of group pursuit
%J Trudy Instituta matematiki i mehaniki
%D 2010
%P 40-51
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a3/
%G ru
%F TIMM_2010_16_1_a3

[1] Pontryagin L. S., Izbrannye nauchnye trudy, v. 2, Nauka, M., 1988, 576 pp. | MR

[2] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[3] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 287 pp. | MR | Zbl

[4] Chikrii A. A., Konfliktno upravlyaemye protsessy, Nauk. dumka, Kiev, 1992, 384 pp.

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

[6] Blagodatskikh A. I., Petrov N. N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov, Izd-vo Udm. un-ta, Izhevsk, 2009, 266 pp. | MR | Zbl

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

[8] Grigorenko N. L., “Igra prostogo presledovaniya-ubeganiya gruppy presledovatelei i odnogo ubegayuschego”, Vest. MGU. Vychisl. matematika i kibernetika, 1983, no. 1, 41–47 | MR | Zbl

[9] Ivanov R. P., “Prostoe presledovanie na kompakte”, Dokl. AN SSSR, 254:6 (1980), 1318–1321 | MR | Zbl

[10] Petrov N. N., Teoriya igr, ucheb. posobie, Izd-vo Udm. un-ta, Izhevsk, 1997, 197 pp. | MR | Zbl

[11] Petrov N. N., “Odna zadacha prostogo presledovaniya s fazovymi ogranicheniyami”, Avtomatika i telemekhanika, 1992, no. 5, 22–26 | Zbl

[12] Bannikov A. S., “Ob odnoi zadache gruppovogo presledovaniya”, Vest. Udm. un-ta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 3, 3–11

[13] Mezentsev A. V., “O nekotorom klasse differentsialnykh igr”, Izv. AN SSSR. Tekhnicheskaya kibernetika, 1971, no. 6, 3–7 | MR | Zbl

[14] Nikolskii M. S., “Nestatsionarnye lineinye differentsialnye igry. I”, Kibernetika, 1970, no. 6, 98–101

[15] Partkhasaratkhi T., Ragkhavan T., Nekotorye voprosy teorii igr dvukh lits, Mir, M., 1974, 29 pp.

[16] Petrov N. N., “Ob upravlyaemosti avtonomnykh sistem”, Differents. uravneniya, 4:4 (1968), 606–617 | Zbl