Geodesic
Solving a~pursuit problem in high-order controlled distributed systems
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 95-110.

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

We study a pursuit problem in controlled systems with high-order distributed parameters. Sufficient conditions are obtained for the possibility of the completion of the pursuit by the finite difference method. We also give computer realizations of the problem by parallel computing. 
@article{MT_2013_16_2_a6,
     author = {M. Sh. Mamatov and Kh. N. Alimov},
     title = {Solving a~pursuit problem in high-order controlled distributed systems},
     journal = {Matemati\v{c}eskie trudy},
     pages = {95--110},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2013_16_2_a6/}
}
TY  - JOUR
AU  - M. Sh. Mamatov
AU  - Kh. N. Alimov
TI  - Solving a~pursuit problem in high-order controlled distributed systems
JO  - Matematičeskie trudy
PY  - 2013
SP  - 95
EP  - 110
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2013_16_2_a6/
LA  - ru
ID  - MT_2013_16_2_a6
ER  - 
%0 Journal Article
%A M. Sh. Mamatov
%A Kh. N. Alimov
%T Solving a~pursuit problem in high-order controlled distributed systems
%J Matematičeskie trudy
%D 2013
%P 95-110
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2013_16_2_a6/
%G ru
%F MT_2013_16_2_a6
M. Sh. Mamatov; Kh. N. Alimov. Solving a~pursuit problem in high-order controlled distributed systems. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 95-110. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a6/

[1] Voevodin Vl. V., Zhumatyi S. A., Vychislitelnoe delo i klasternye sistemy, Izd-vo MGU, M., 2007

[2] Gergel V. P., Strongin R. G., Osnovy parallelnykh vychislenii dlya mnogoprotsessornykh vychislitelnykh sistem, Izd-vo NNGU, Nizhnii Novgorod, 2003

[3] Gregori R. Endryus, Osnovy mnogopotochnogo, parallelnogo i raspredelennogo programmirovaniya, Izd-vo “Vilyams”, M., 2003

[4] Ilin V. A., Moiseev E. I., “Optimalnoe granichnoe upravlenie smescheniem na odnom kontse pri svobodnom vtorom kontse i otvechayuschee emu raspredelenie polnoi energii struny”, Dokl. RAN, 400:5 (2005), 587–591 | MR

[5] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Ucheb. posobie, Nauka, Moskva, 1973 | MR

[6] Mamatov M. Sh., “O primenenii metoda konechnykh raznostei k resheniyu zadachi presledovaniya v sistemakh s raspredelennymi parametrami”, Avtomat. i telemekh., 2009, no. 8, 123–132 | MR | Zbl

[7] Mamatov M. Sh., “K teorii differentsialnykh igr presledovaniya v sistemakh s raspredelennymi parametrami”, Avtomat. i vychislitel. tekhn., 2009, no. 1, 5–14

[8] Mamatov M. Sh., Tukhtasinov M., “O zadache presledovaniya v raspredelennykh upravlyaemykh sistemakh”, Kibernet. i sistem. anal., 45:2 (2009), 153–158 | MR | Zbl

[9] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1989 | MR | Zbl

[10] Osipov Yu. S., “Pozitsionnoe upravlenie v parabolicheskikh sistemakh”, Prikl. matem. i mekh., 41:2 (1977), 195–201 | MR

[11] Osipov Yu. S., Korotkii A. I., “Approksimatsiya v zadachakh pozitsionnogo upravleniya parabolicheskimi sistemami”, Prikl. matem. i mekh., 42:4 (1978), 599–605 | MR

[12] Osipov Yu. S., Pandolfi L., Maksimov V. I., “Zadacha robastnogo granichnogo upravleniya: sluchai kraevykh uslovii Dirikhle”, Dokl. RAN, 374:3 (2000), 310–312 | MR | Zbl

[13] Satimov N. Yu., Mamatov M. Sh., “Ob odnom klasse lineinykh differentsialnykh i diskretnykh igr mezhdu gruppami presledovatelei i ubegayuschikh”, Differents. uravneniya, 26:9 (1990), 1541–1551 | MR | Zbl

[14] Satimov N. Yu., Tukhtasinov M., “O nekotorykh igrovykh zadachakh v raspredelennykh upravlyaemykh sistemakh”, Prikl. matem. i mekh., 69:6 (2005), 986–992 | MR | Zbl

[15] Satimov N. Yu., Tukhtasinov M., “Ob igrovykh zadachakh na fiksirovannom otrezke v upravlyaemykh evolyutsionnykh uravneniyakh pervogo poryadka”, Matem. zametki, 80:4 (2006), 613–626 | DOI | MR | Zbl

[16] Soulev V. K., Integrirovanie uravnenii parabolicheskogo tipa metodom setok, Fizmatgiz, M., 1960 | MR

[17] Tikhomirov V. V., “Volnovoe uravnenie s granichnym upravleniem pri uprugom zakreplenii. I”, Differents. uravneniya, 38:3 (2002), 393–403 | MR | Zbl

[18] Tukhtasinov M., Mamatov M. Sh., “O zadachakh presledovaniya v upravlyaemykh raspredelennykh sistemakh”, Matem. zametki, 84:2 (2008), 273–280 | DOI | MR | Zbl

[19] Tukhtasinov M., Mamatov M. Sh., “O zadachakh perekhoda v upravlyaemykh sistemakh”, Differents. uravneniya, 45:3 (2009), 425–430 | MR | Zbl

[20] Tartyshnikov E. E., Metody chislennogo analiza, Izdatelskii tsentr “Akademiya”, M., 2007

[21] Browder F., “Linear parabolic differential equations of arbitrary order; general boundary-value problems for elliptic equations”, Proc. Nat. Acad. Sci. U.S.A., 39:3 (1953), 185–190 | DOI | MR | Zbl

[22] Grama A., Gupta. A., Karypis G., Kumar V., Introduction to Parallel Computing, Addison Wesley, Harlow, 2003