On the modified third method in the pursuit problem for differential-difference equations of neutral type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 21-33.

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

In this paper, we study linear differential games described by a system of linear differential-difference equations of neutral type under geometric constraints on the controls of the players. We give several scheme for getting enough conditions for solvability of the linear problem pursuit.
Keywords: differential games, the pursuit problem, differential-difference equations of neutral type, terminal set, pursuer, evader, controls.
@article{IVM_2021_11_a2,
     author = {N. A. Mamadaliev and T. T. Ibaydullaev},
     title = {On the modified third method in the pursuit problem for differential-difference equations of neutral type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {21--33},
     publisher = {mathdoc},
     number = {11},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_11_a2/}
}
TY  - JOUR
AU  - N. A. Mamadaliev
AU  - T. T. Ibaydullaev
TI  - On the modified third method in the pursuit problem for differential-difference equations of neutral type
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 21
EP  - 33
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_11_a2/
LA  - ru
ID  - IVM_2021_11_a2
ER  - 
%0 Journal Article
%A N. A. Mamadaliev
%A T. T. Ibaydullaev
%T On the modified third method in the pursuit problem for differential-difference equations of neutral type
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 21-33
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_11_a2/
%G ru
%F IVM_2021_11_a2
N. A. Mamadaliev; T. T. Ibaydullaev. On the modified third method in the pursuit problem for differential-difference equations of neutral type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 21-33. http://geodesic.mathdoc.fr/item/IVM_2021_11_a2/

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

[2] Satimov N. Yu., Metody resheniya zadachi presledovaniya v teorii differentsialnykh igr, Izd-vo NUUz, Tashkent, 2003

[3] Grigorenko H. L., Matematicheskie metody upravleniya neskolkimi dinamicheskimi protsessami, MGU, M., 1990

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

[5] Pshenichnyi B. N., “Lineinye differentsialnye igry”, Avtomatika i telemekhanika, 1968, no. 1, 65–78 | Zbl

[6] Azamov A., “On the quality problem for simple pursuit games with constraint”, Serdica Math. J., 12:1 (1986), 38–43 | Zbl

[7] Nikolskii M. S., “O zadache presledovaniya pri razlichnykh ogranicheniyakh na upravleniya dogonyayuschego i ubegayuschego”, Teoriya optimalnykh reshenii, Izdanie in-ta kibernetiki, Kiev, 1975, 59–66

[8] Samatov B. T., “On a pursuit-evasion problem under a linear change of the pursuer-controls”, Siberian Adv. Math., 23:1 (2013), 294–302 | DOI

[9] Samatov B. T., “The pursuit-evasion problem under integral-geometric constraints on pursuier controls”, Autom. Remote Control, 74:7 (2013), 1072–1081 | DOI | Zbl

[10] Mamadaliev N. A., “O zadachakh presledovaniya v lineinykh differentsialnykh igrakh pri nalichii zapazdyvanii”, Izv. vuzov. Matem., 2010, no. 6, 16–22 | Zbl

[11] Mamadaliev N., “Zadacha presledovaniya dlya lineinykh igr s integralnymi ogranicheniyami na upravleniya igrokov”, Izv. vuzov. Matem., 2020, no. 3, 12–28 | Zbl

[12] Mamadaliev N., “Lineinye differentsialnye igry s integralnymi ogranicheniyami pri nalichii zapazdyvaniya”, Matem. zametki, 91:5 (2012), 750–760 | Zbl

[13] Mamadaliev N., “O zadache presledovaniya dlya lineinykh differentsialnykh igr s razlichnymi ogranicheniyami na upravleniya igrokov”, Differents. uravneniya, 48:6 (2012), 860–873 | Zbl

[14] Mamadaliev N., “Ob odnoi zadache presledovaniya s integralnymi ogranicheniyami na upravleniya igrokov”, Sib. matem. zhurn., 56:1 (2015), 129–148 | Zbl

[15] Krasovskii N. N., Osipov Yu. S., “Lineinye differentsialno-raznostnye igry”, Dokl. AN SSSR, 197:4 (1971), 777–780 | Zbl

[16] Kryazhimskii A. V., Osipov Yu. S., “Differentsialno-raznostnaya igra sblizheniya s funktsionalnym tselovym mnozhestvom”, Prikl. matem. i mekhanika, 37:1 (1973), 3–13 | Zbl

[17] Nikolskii M. S., “Lineinye differentsialnye igry presledovaniya pri nalichii zapazdyvanii”, Dokl. AN SSSR, 197:5 (1971), 1018–1021 | Zbl

[18] Chikrii A. A., Chikrii G. Ts., “Gruppovoe presledovanie v differentsialno-raznostnykh igrakh”, Differents. uravneniya, 20:5 (1984), 802–810 | Zbl

[19] Baranovskaya L. V., “Metod razreshayuschikh funktsii dlya odnogo klassa zadach presledovaniya”, Vostochno-Evropeisk. zhurn. peredovykh tekhnologii, 2/4:74 (2015), 4–8

[20] Tukhtasinov M., “$\varepsilon$-Positional Strategy in the Second Method of Differential Games of Pursuit”, Diff. Equat. and Dynamical Syst., 268 (2018), 169–182 | DOI | Zbl

[21] Tukhtasinov M., “Lineinaya differentsialnaya igra presledovaniya s impulsnym i integralno-ogranichennymi upravleniyami igrokov”, Tr. IMM UrO RAN, 22, no. 3, 2016, 273–282

[22] Chikrii A. A., Matichin I. I., “Lineinye differentsialnye igry s impulsnym upravleniem igrokov”, Tr. IMM UrO RAN, 11, no. 1, 2005, 212–224

[23] Belousov A. A., “Differentsialnye igry s integralnymi ogranicheniyami i impulsnymi upravleniyami”, Dokl. NAN Ukrainy, 2013, no. 11, 37–42 | Zbl

[24] Ukhobotov V. I., Troitskii A. A., “Ob odnoi zadache impulsnogo presledovaniya”, Vestn. Yuzhno-Uralsk. un-ta. Ser. Matem. Mekhanika. Fizika, 5:2 (2013), 79–87 | Zbl

[25] Azamov A., Samatov B. T., “O modifitsirovannom tretem metode v zadachakh presledovaniya”, Neklassicheskie zadachi matematicheskoi fiziki, FAN, Tashkent, 1985, 174–184

[26] Ushakov V. N., “Ekstremalnye strategii v differentsialnykh igrakh s integralnymi ogranicheniyami”, Prikl. matem. i mekhanika, 36:1 (1972), 15–22

[27] Chikrii A. A., Bezmagorychnyi V. V., “Metod razreshayuschikh funktsii v lineinykh differentsialnykh igrakh s integralnymi ogranicheniyami”, Avtomatika, 1993, no. 4, 26–36

[28] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Nauka, M., 1967

[29] Blagodatskikh V. I., Vvedenie v optimalnoe upravlenie, Vyssh. shk., M., 2004

[30] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977