Geodesic
A method for solving a boundary value problem for a nonlinear control system with incomplete information
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1393-1407 Cet article a éte moissonné depuis la source Math-Net.Ru

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An easy-to-implement numerical method is proposed for synthesizing a feedback control function that transfers a wide class of nonlinear stationary systems from an initial state to a given terminal state with allowance for measured data. A constructive criterion is obtained for choosing terminal states for which this transfer is guaranteed. The problem of an interorbital flight is considered and numerically simulated. 
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A. N. Kvitko. A method for solving a boundary value problem for a nonlinear control system with incomplete information. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1393-1407. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a4/

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

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

[3] Gusar V. V., “Ob odnoi zadache splain-upravleniya”, Differents. ur-niya, 1998, no. 9, 1475–1481 | MR

[4] Chernousko F. L., “Dekompozitsiya i sintez upravleniya v nelineinykh dinamicheskikh sistemakh”, Tr. Matem. in-ta RAN, 211, M., 1995, 457–473 | MR

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

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

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

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

[9] Luenberger D. G., Determing the state linear system with observers low dynamic order, Ph. D. Diss., Stanford Univ., 1963

[10] Luenberger D. G., “Observers for multivariable systems”, IEEE Trans. Automatic Control, 1966, 190–197 | DOI

[11] Trin H., Ha Q. P., “Design of linear functional observers for linear systems with unknown inmputs”, Internat. J. Systems Sci, 31:6 (2000), 741–749 | DOI | Zbl

[12] Roman J. R., Bullok T. E., “Design of minimal-order stable observes for linear functions of the state via realization theory”, IEEE Trans. Automatic Control, 20 (1975), 613–622 | DOI | MR | Zbl

[13] Bhattachargun S. P., “Observer design for linear system with unknown input”, IEEE Trans. Automatic Control, 23 (1978), 483–484 ; Bol. Unione mat. Ital., 5:1 (1986), 127–137 | DOI | MR | MR

[14] Korovin S. K., Fomichev V. V., “Eksponentsialnye nablyudateli bilineinykh sistem na ploskosti”, Differents. ur-niya, 37:12 (2001), 1605–1612 | MR

[15] Korovin S. K., Fomichev V. V., “Asimptoticheskie nablyudateli dlya nekotorykh klassov bilineinykh sistem s lineinym vkhodom”, Dokl. RAN. Teoriya upravleniya, 398:1 (2004), 38–43 | MR

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

[17] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, M., 1959 | MR

[18] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968 | MR