Differential pursuit games of neutral type with integral restrictions on player controls
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 4, pp. 45-68.

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In this paper, we study linear differential games described by a system of linear differential-difference equations of neutral type under integral constraints on the controls of the players. We obtain new sufficient conditions on parameters of the process guaranteeing finishing the game in a definite finite time.
Keywords: differential games, the pursuit problem, differential-difference equations of neutral type, pursuer, evader, controls.
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Numanjon A. Mamadaliev; Hamdam Ya. Mustapokulov; Muhammadsodiq M. Abdumannopov. Differential pursuit games of neutral type with integral restrictions on player controls. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 4, pp. 45-68. http://geodesic.mathdoc.fr/item/MGTA_2024_16_4_a2/

[1] Azamov A., Kuchkarov A.Sh., Samatov B.T., “O svyazi mezhdu zadachami presledovaniya, upravlyamosti i ustoichivosti v tselom v lineinykh sistemakh s raznotipnymi ogranicheniyami”, Prikladnaya matematika i mekhanika, 71:2 (2005), 259–263

[2] Azimov A.Ya., “Ob odnom sposobe presledovaniya v lineinykh differentsialnykh igrakh s obschimi integralnymi ogranicheniyami”, Izv. AN SSSR, Tekhn. kibernetika, 1974, no. 2, 31–35 | Zbl

[3] Azimov A.Ya., Guseinov F.V., “O nekotorykh klassakh differentsialnykh igr s obschimi integralnymi ogranicheniyami”, Izv. AN SSSR, Tekhn. kibernetika, 1972, no. 3, 9–10

[4] Bellman R., Kuk K., Differentsialno - raznostnye uravneniya, Mir, M., 1967

[5] Belousov A.A., “Metod razreshayuschikh funktsii dlya differentsialnykh igr s integralnymi ogranicheniyami”, Teoriya optimalnykh reshenii, 2010, no. 2, 10–16

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

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

[8] Grigorenko N.L., “O strukture odnogo klassa differentsialnykh igr s obschimi integralnymi ogranicheniyami”, Upravlyaemye sistemy, 1974, no. 12, 46–53 | Zbl

[9] Kolmogorov A.N., Fomin S.V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972 | MR

[10] Krasovskii N.N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970

[11] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR

[12] Krasovskii N.N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985 | MR

[13] Kuratovskii K., Topologiya, v. 2, Mir, M., 1969

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

[15] Mamadaliev N., “Ob odnoi lineinoi zadache presledovaniya pri nalichii zapazdyvaniya”, Sibirskii zhurnal industrialnoi matematiki, 13:3 (2010), 86–101 | MR

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

[17] Mamadaliev N., “O zadachakh presledovaniya v lineinykh differentsialnykh igrakh pri nalichii zapazdyvanii”, Izvestiya vuzov. Matematika, 2010, no. 6, 16–22 | Zbl

[18] Mamadaliev N.A., Mustapokulov Kh.Ya., Abdualimova G.M., “Metod razreshayuschikh funktsii dlya resheniya zadachi presledovaniya pri integralnykh ogranicheniyakh na upravleniya”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 33:1 (2023), 103–118 | MR | Zbl

[19] Mamadaliev N., “Lineinye differentsialnye igry s integralnymi ogranicheniyami pri nalichii zapazdyvanii”, Matematicheskie zametki, 2012, no. 5, 750–760 | DOI | Zbl

[20] Mamadaliev N.A., “Zadacha ppesledovaniya dlya lineinykh igr s integralnymi ogranicheniyami na upravleniya igrokov”, Izvestiya vuzov. Matematika, 2020, no. 3, 12–28 | Zbl

[21] Mamadaliev N.A., Ibaidullaev T.T., “Modifikatsiya tretego metoda presledovaniya dlya differentsialno-raznostnykh uravnenii neitralnogo tipa”, Izvestiya vuzov. Matematika, 2021, no. 11, 21–33 | Zbl

[22] Mamadaliev N.A., Khaiitkulov B.Kh., “Polnoe reshenie odnogo klassa differentsialnykh igr presledovaniya s integralnymi ogranicheniyam i impulsnym upravleniem”, Izvestiya vuzov. Matematika, 2022, no. 3, 28–37 | Zbl

[23] Mezentsev A.V., Differentsialnye igry s integralnymi ogranicheniyami na upravleniya, Izd-vo MGU, M., 1988

[24] Mukhsinov E.M., “Ob odnoi differentsialnoi igre neitralnogo tipa s integralnymi ogranicheniyami v gilbertovom prostranstve”, Ufimskii matematicheskii zhurnal, 14:3 (2022), 90–100 | Zbl

[25] Nikolskii M.S., “Pryamoi metod v lineinykh differentsialnykh igrakh s obschimi integralnymi ogranicheniyami”, Differentsialnye uravneniya, 8:6 (1972), 964–971 | Zbl

[26] Nikolskii M.S., “Lineinye differentsialnye igry presledovaniya s integralnymi ogranicheniyami”, Differentsialnye uravneniya, 28:2 (1992), 219–223 | MR

[27] Petrov N.N., “Kvazilineinye konfliktno- upravlyaemye protsessy s dopolnitelnymi ogranicheniyami”, Prikladnaya matematika i mekhanika, 57:6 (1993), 61–68 | MR | Zbl

[28] Petrov N.N., “Ob odnoi zadache presledovaniya so mnogimi ubegayuschimi”, Vestnik Udmurtskogo un-ta, 2000, no. 1, 131–136

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

[30] Pontryagin L.S., “K teorii differentsialnykh igr”, Uspekhi matematicheskikh nauk, 21:4 (1966), 219–274 | MR | Zbl

[31] Pontryagin L.S., “Lineinye differentsialnye igry presledovaniya”, Matematicheskii sbornik, 3:7 (1980), 307–330

[32] Pshenichnyi B.N., Onopchuk Yu.N., “Lineinye differentsialnye igry s integralnymi ogranicheniyami”, Izv. AN SSSR, Tekhn. kibernetika, 1968, no. 1, 13–22 | Zbl

[33] Rappoport I.S., “K resheniyu zadachi presledovaniya s integralnymi ogranicheniyami na upravleniya”, Teoriya optimalnykh reshenii, 2018, no. 17, 10–18

[34] Samatov B.A., “Metod razreshayuschikh funktsii dlya resheniya zadachi presledovaniya pri integralnykh ogranicheniyakh na upravleniya”, Problemy upravleniya i informatiki, 2013, no. 4, 16–32

[35] Satimov N.Yu., Fazylov A.Z., Khamdamov A.A., “O zadachakh presledovaniya i ukloneniya v differentsialnykh i diskretnykh igrakh mnogikh lits s integralnymi ogranicheniyami”, Differentsialnye uravneniya, 20:8 (1984), 1388–1396 | MR | Zbl

[36] Satimov N.Yu., Metody resheniya zadachi presledovaniya v teorii differentsialnykh igr, Nats. bibl. Uzbekistana im. Alishera Navoi, Tashkent, 2019

[37] Tukhtasinov M., “Lineinaya differentsialnaya igra presledovaniya s impulsnymi i integralno-ograniennmi pralenimi igroko”, Trudy IMM UrO RAN, 22, no. 3, 2016, 273–282 | MR

[38] Ushakov V.N., “Ekstremalnye strategii v differentsialnykh igrakh s integralnymi ogranicheniyami”, Prikladnaya matematika i mekhanika, 36:1 (1972), 15–23 | Zbl

[39] Chikrii A.A., Konfliktno upravlyaemye protsessy, Naukova dumka, Kiev, 1992

[40] Chikrii A.A., Bezmagorichnyi V.V., “Metod razreshayuschikh funktsii dlya lineinykh differentsialnykh igrakh s integralnymi ogranicheniyami”, Avtomatika, 1993, no. 4, 26–30 | MR

[41] Chikrii A.A., Belousov A.A., “O lineinykh differentsialnykh igrakh s integralnymi ogranicheniyami”, Trudy Instituta matematiki i mekhaniki UrO RAN, 15, no. 4, 2009, 290–301

[42] Kisieleqier M., “Differential inclusions and optimal control”, Mathematics and Its Applications, 44, Kluwer Acad. Publ., Boston, 1991 | MR

[43] Tukhtasinov M., Mustapokulov Kh.Ya., “$\varepsilon-$Positional Strategies In Theory Of Differential Pursuit Games And Invariance Of Constant Multivalued Mappings In Heat-Conductivity Problems”, Journal of Mathematical Sciences, 265:1 (2022) | DOI | MR | Zbl