Geodesic
Method of Controlled Models in the Problem of Reconstructing a~Boundary Input
Informatics and Automation, Optimal control, Tome 262 (2008), pp. 178-186.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of dynamic reconstruction of boundary controls in a nonlinear parabolic equation is considered. In the case of a control concentrated in the Neumann boundary conditions, a solution algorithm is described, which is stable with respect to the information noise and calculation errors. The algorithm is based on the construction of feedback-controlled auxiliary models. 
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V. I. Maksimov. Method of Controlled Models in the Problem of Reconstructing a~Boundary Input. Informatics and Automation, Optimal control, Tome 262 (2008), pp. 178-186. http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a12/

[1] Alifanov O. M., Artyukhin E. A., Rumyantsev S. V., Ekstremalnye metody resheniya nekorrektnykh zadach, Nauka, M., 1988 | MR | Zbl

[2] Gusev M. I., Kurzhanskii A. B., “Obratnye zadachi dinamiki upravlyaemykh sistem”, Mekhanika i nauchno-tekhnicheskii progress. T. 1: Obschaya i prikladnaya mekhanika, Nauka, M., 1987, 187–195 | MR

[3] Kryazhimskii A. V., Osipov Yu. S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Ser. tekhn. kibern., 1983, no. 2, 51–60 | MR | Zbl

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

[5] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., Zadachi dinamicheskoi regulyarizatsii dlya sistem s raspredelennymi parametrami, Izd. In-ta matematiki i mekhaniki UrO RAN, Sverdlovsk, 1991

[6] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, Izd. In-ta matematiki i mekhaniki UrO RAN, Ekaterinburg, 2000

[7] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., “Dinamicheskie obratnye zadachi dlya parabolicheskikh sistem”, Dif. uravneniya, 36:5 (2000), 579–597 | MR | Zbl

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

[9] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR

[10] Maksimov V., Pandolfi L., “Dynamical reconstruction of inputs for contraction semigroup systems: boundary input case”, J. Optim. Theory and Appl., 103:2 (1999), 401–420 | DOI | MR | Zbl

[11] Osipov Yu. S., Pandolfi L., Maksimov V. I., “Problems of dynamical reconstruction and robust boundary control: the case of the Dirichlet boundary conditions”, J. Inverse and Ill-Posed Probl., 9:2 (2001), 149–162 | MR | Zbl

[12] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR

[13] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[14] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972 | MR | Zbl

[15] Osipov Yu. S., Okhezin S. P., “K teorii differentsialnykh igr v parabolicheskikh sistemakh”, DAN SSSR, 226:6 (1976), 1267–1270 | MR | Zbl