Function defect in differential games with terminal pay
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 2, pp. 99-128 Cet article a éte moissonné depuis la source Math-Net.Ru

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The antagonistic differential game of two players with terminal pay function is considered. Function defect conception is suggested for functions connected with the coast of the game.
Keywords: game problem, control, conflict controlled system, Hamiltonian, stability defect, stable bridge.
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Vladimir N. Ushakov; Alexandr A. Uspenskiy. Function defect in differential games with terminal pay. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 2, pp. 99-128. http://geodesic.mathdoc.fr/item/MGTA_2010_2_2_a4/

[1] Gusev M. I., “Otsenki mnozhestv dostizhimosti mnogomernykh upravlyaemykh sistem s nelineinymi perekrëstnymi svyazyami”, Tr. IMM UrO RAN, 15, no. 4, 2009, 82–94

[2] Demyanov V. F., Rubinov A. M., Osnovy negladkogo analiza i kvazidifferentsialnoe ischislenie, Nauka, M., 1990 | MR

[3] Krasovskii N. N., “Igrovye zadachi dinamiki. I”, Izv. AN SSSR. Tekhn. kibernetika, 1969, no. 5, 3–12 | MR

[4] Krasovskii N. N., Subbotin A. I., “Smeshannoe upravlenie v differentsialnoi igre”, Dokl. AN SSSR, 188:4 (1969), 745–747 | MR

[5] Krasovskii N. N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970 | MR | Zbl

[6] Krasovskii N. N., Subbotin A. I., “O strukture differentsialnykh igr”, Dokl. AN SSSR, 190:3 (1970), 523–526 | MR

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

[8] Krasovskii N. N., “K zadache unifikatsii differentsialnykh igr”, Dokl. AN SSSR, 226:6 (1976), 1260–1263 | MR

[9] Krasovskii N. N., “Unifikatsiya differentsialnykh igr”, Igrovye zadachi upravleniya, Tr. In-ta matematiki i mekhaniki, 24, UNTs AN SSSR, Sverdlovsk, 1977, 32–45 | MR

[10] Kurzhanskii A. B., “Printsip sravneniya dlya uravnenii tipa Gamiltona–Yakobi v teorii upravleniya”, Tr. IMM UrO RAN, 12, no. 1, 2006, 173–183 | MR | Zbl

[11] Nikolskii M. S., “Ob alternirovannom integrale L. S. Pontryagina”, Mat. sb., 116(158):1 (1981), 136–144 | MR | Zbl

[12] Osipov Yu. S., “Alternativa v differentsialno-raznostnoi igre”, Dokl. AN SSSR, 197:5 (1971), 619–624 | Zbl

[13] Petrov N. N., “O suschestvovanii znacheniya igry presledovaniya”, Dokl. AN SSSR, 190:6 (1970), 1289–1291 | MR | Zbl

[14] Pontryagin L. S., “O lineinykh differentsialnykh igrakh. II”, Dokl. AN SSSR, 175:4 (1967), 764–766 | Zbl

[15] Pontryagin L. S., “Matematicheskaya teoriya optimalnykh protsessov i differentsialnye igry”, Trudy MIAN, 169, M., 1985, 119–158 | MR | Zbl

[16] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981 | MR

[17] Subbotin A. I., Subbotina N. N., “Funktsiya optimalnogo rezultata v zadache upravleniya”, Dokl. AN SSSR, 266:2 (1982), 294–299 | MR | Zbl

[18] Subbotin A. I., Obobschennye resheniya uravnenii v chastnykh proizvodnykh pervogo poryadka, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003 | Zbl

[19] Tarasev A. M., Ushakov V. N., O postroenii stabilnykh mostov v minimaksnoi igre sblizheniya-ukloneniya, Dep. v VINITI, No 2454-83, Sverdlovsk, 1983

[20] Tarasev A. M., Ushakov V. N., Khripunov A. P., “Ob odnom vychislitelnom algoritme resheniya igrovykh zadach upravleniya”, Prikl. matematika i mekhanika, 51:2 (1987), 216–222 | MR | Zbl

[21] Ukhobotov V. I., “Analiticheskaya skhema postroeniya stabilnykh mostov dlya operatorov programmnogo pogloscheniya s invariantnymi semeistvami mnozhestv”, Izvestiya Instituta matematiki i informatiki UdGU (Izhevsk), 2005, no. 2(32), 23–34

[22] Ushakov V. N., Latushkin Ya. A., “Defekt stabilnosti mnozhestv v igrovykh zadachakh upravleniya”, Tr. In-ta matematiki i mekhaniki, 12, no. 2, UrO RAN, Ekaterinburg, 2006, 178–194 | MR | Zbl

[23] Ushakov V. N., Malëv A. G., “K voprosu o defekte stabilnosti mnozhestv v igrovoi zadache o sblizhenii”, Tr. In-ta matematiki i mekhaniki, 16, no. 1, 2010, 199–222

[24] Filippova T. F., “Differentsialnye uravneniya ellipsoidalnykh otsenok mnozhestv dostizhimosti nelineinoi dinamicheskoi upravlyaemoi sistemy”, Tr. IMM UrO RAN, 16, no. 1, 2010, 223–232

[25] Chernousko F. L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem, Nauka, M., 1988 | MR

[26] Guseinov H. G., Subbotin A. I., Ushakov V. N., “Derivatives for Multivalued Mappings with Applications to Game-Theoretical Problems of Control”, Problems Control Inform. Theory, 14:6 (1985), 405–419 | MR | Zbl

[27] Kurzhanski A. B., Valyi I., Ellipsoidal calculus for estimation and control, Birkhauser, Boston, 1997 | MR | Zbl

[28] Osipov Yu. S., Kryazhimski A. V., Inverse problems for ordinary differential equations: dynamical solutions, Gordon and Breach, London, 1995 | MR | Zbl

[29] Petrosjan L., Differential Games of Pursuit, World Scientific, Singapore, 1993 | MR

[30] Ushakov V. N., Taras'ev A. M., Tokmantsev T. B., Uspenskii A. A., “On procedures for constructing solutions in differential games on a finite interval of time”, Journal of Mathematical Sciences, 139:5 (2006), 6954–6975 | DOI | MR | Zbl

[31] Ushakov V. N., Brykalov S. A., Latushkin Y. A., “Stable and unstanble sets in problems of conflict control”, Functional Differential Equations, 15:3–4 (2008), 309–338 | MR | Zbl