Geodesic
A method for solving a boundary problem for a nonlinear controlled system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1241-1250 
A. N. Kvitko. A method for solving a boundary problem for a nonlinear controlled system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1241-1250. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a7/
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     title = {A~method for solving a~boundary problem for a~nonlinear controlled system},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An algorithm is proposed for constructing a control function that transfers a wide class of nonlinear systems of ordinary differential equations from an initial state to an arbitrarily small neighborhood of a given terminal state. The algorithm is convenient for numerical implementation. Taking into account the restrictions on the control and phase coordinates, a constructive criterion is obtained for choosing terminal states for which this transfer is possible. The problem of an interorbital flight is considered and modeled numerically.

[1] Kallman R.,Falb P., Arbib M., Ocherki po matematicheskoi teorii sistem, Mir, M., 1971 | MR

[2] Zubov V. I., Lektsii po teorii upravleniya, Nauka, M., 1975 | MR | Zbl

[3] Komarov V. A., “Sintez ogranichennykh upravlenii dlya nelineinykh sistem”, Avtomatika i telemekhan., 1993, no. 2, 76–82 | MR | Zbl

[4] Gusar V. V., “Ob odnoi zadache splain upravleniya”, Differents. ur-niya, 1988, no. 9, 1475–1481 | MR

[5] Chernousko F. L., “Dekompozitsiya i sintez upravleniya v nelineinykh dinamicheskikh sistemakh”, Tr. Matem. in-ta RAN, 211, M., 1995, 457–472 | MR | Zbl

[6] Chernousko F. L., “Upravlenie sistemoi s odnoi stepenyu svobody pri ogranicheniyakh na upravlyayuschuyu silu i skorost ee izmeneniya”, Dokl. RAN, 1999, no. 4, 464–472 | MR

[7] Kovrizhkin O. G., Kramarenko E. L., “Vstrechnyi metod resheniya zadachi upravleniya konechnym sostoyaniem”, Avtomatika i telemekhan., 1994, no. 3, 37–42 | MR | Zbl

[8] Korobov V. I., Sklyar G. M., “O mnozhestve pozitsionnykh ogranichennykh upravlenii, reshayuschikh zadachu sinteza”, Dokl. AN SSSR, 312:6 (1990), 1304–1308 | MR | Zbl

[9] Kvitko A. N., “Ob odnom metode postroeniya programmnykh dvizhenii”, Prikl. matem. i mekhan., 65:3 (2001), 392–399 | MR | Zbl

[10] Kvitko A. N., “Ob odnoi zadache upravleniya”, Differents. ur-niya, 40:6 (2004), 740–746 | MR | Zbl

[11] Barbashin E. A., Vvedenie v teoriyu ustoichivosti, Nauka, M., 1967 | Zbl

[12] Krasovskii H. H., Teoriya upravleniya dvizheniem, Nauka, M., 1968