On a~supplement to the stability property in differential games

V. N. Ushakov ; A. A. Uspenskii

Informatics and Automation, Differential equations and topology. II, Tome 271 (2010), pp. 299-318.

Résumé

The stability property in a game problem of approach “at the final instant” is studied. The concept of the stability defect of sets in the position space of a game is analyzed.

Bibliographie

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

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

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

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

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

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

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

[8] Guseĭnov H.G., Subbotin A.I., Ushakov V.N., “Derivatives for multivalued mappings with applications to game-theoretical problems of control”, Probl. Control and Inf. Theory, 14:3 (1985), 155–167 | MR | Zbl

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

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

[11] Kurzhanskii A.B., “Alternirovannyi integral Pontryagina v teorii sinteza upravlenii”, Tr. MIAN, 224, 1999, 234–248 | MR | Zbl

[12] Kurzhanskii A.B., “Printsip sravneniya dlya uravnenii tipa Gamiltona–Yakobi v teorii upravleniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 12, no. 1, 2006, 173–183 | Zbl

[13] Osipov Yu.S., “Alternativa v differentsialno-raznostnoi igre”, DAN SSSR, 197:5 (1971), 1022–1025 | MR | Zbl

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

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

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

[17] Tarasev A.M., Ushakov V.N., O postroenii stabilnykh mostov v minimaksnoi igre sblizheniya–ukloneniya, Dep. v VINITI, No2454-83, Sverdlovsk, 1983, 61 pp.

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

[19] Tarasev A.M., Tokmantsev T.B., Uspenskii A.A., Ushakov V.N., “O protsedurakh postroeniya reshenii v differentsialnykh igrakh na konechnom promezhutke vremeni”, Sovr. matematika i ee pril., 23 (2005), 123–144 | MR

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

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

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