Geodesic
On reconstruction of unknown characteristics of a distributed system using a regularized extremal shift
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 3, pp. 170-184
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The problem of stable dynamical reconstruction of unknown characteristics in a distributed system described by a pair of differential equations is considered. The aim of the paper is to construct a solution algorithm for this problem. The proposed algorithm is based on Yu. S. Osipov's theory of dynamic inversion and N. N. Krasovskii's extremal shift method.
Keywords: distributed systems, extremal shift
Mots-clés : reconstruction. 
@article{TIMM_2009_15_3_a12,
     author = {V. I. Maksimov},
     title = {On reconstruction of unknown characteristics of a~distributed system using a~regularized extremal shift},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {170--184},
     year = {2009},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_3_a12/}
}
TY  - JOUR
AU  - V. I. Maksimov
TI  - On reconstruction of unknown characteristics of a distributed system using a regularized extremal shift
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2009
SP  - 170
EP  - 184
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2009_15_3_a12/
LA  - ru
ID  - TIMM_2009_15_3_a12
ER  - 
%0 Journal Article
%A V. I. Maksimov
%T On reconstruction of unknown characteristics of a distributed system using a regularized extremal shift
%J Trudy Instituta matematiki i mehaniki
%D 2009
%P 170-184
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2009_15_3_a12/
%G ru
%F TIMM_2009_15_3_a12
V. I. Maksimov. On reconstruction of unknown characteristics of a distributed system using a regularized extremal shift. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 3, pp. 170-184. http://geodesic.mathdoc.fr/item/TIMM_2009_15_3_a12/

[1] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978, 208 pp. | MR

[2] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981, 400 pp. | MR

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

[4] Osipov Yu. S., Kryazhimskii A. V., Inverse problems of ordinary differential equations: dynamical solution, Gordon and Breach, London, 1995, 673 pp. | MR | Zbl

[5] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, In-t matematiki i mekhaniki UrO RAN, Ekaterinburg, 2000, 306 pp.

[6] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., “Metod ekstremalnogo sdviga N. N. Krasovskogo i zadachi granichnogo upravleniya”, Avtomatiki i telemekhanika, 4 (2009), 18–30

[7] Osipov Yu. S., Korotkii A. I., “Dinamicheskoe modelirovanie parametrov v giperbolicheskikh sistemakh”, Izv. AN SSSR. Tekhn. kibernetika, 1991, no. 2, 154–164 | MR | Zbl

[8] Korotkii A. I., “Vosstanovlenie upravlenii i parametrov dinamicheskikh sistem pri nepolnoi informatsii”, Izv. vyssh. ucheb. zavedenii. Matematika, 1998, no. 11(438), 47–55 | MR | Zbl

[9] Rozenberg V. L., “Zadacha dinamicheskogo vosstanovleniya funktsii istochnika v parabolicheskom uravnenii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 3, Ekaterinburg, 1995, 183–201 | MR | Zbl

[10] Tsepelev I. A., “Dinamicheskoe vosstanovlenie mnozhestva parametrov v kraevoi zadache Gursa–Darbu”, Tr. In-ta matematiki i mekhaniki UrO RAN, 5, Ekaterinburg, 1998, 319–327 | Zbl

[11] Blizorukova M., “Positional modeling in a system with time delay”, Analysis and optimization of differential systems, eds. V. Barbu et., Kluwer Acad. Publishers, Boston, MA, 2003, 49–55 | MR | Zbl

[12] Vasileva E. V., Maksimov V. I., “O dinamicheskoi rekonstruktsii upravleniya v differentsialnom uravnenii s pamyatyu”, Differents. uravneniya, 35:6 (1999), 803–814 | MR

[13] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 451 pp. | MR | Zbl

[14] Caginalp G., “An analysis of a phase field model of a free boundary”, Arch. Rat. Mech. Analysis, 92 (1986), 205–245 | DOI | MR | Zbl

[15] Heinkenschloss M., Tröltzsch F., “Analysis of the Lagrange-SQP-Newton method for the control of a phase field equation”, Control and Cybernetics, 28:2 (1999), 177–211 | MR | Zbl

[16] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973, 452 pp. | MR

[17] Hoffman K.-H., Jiang L. S., “Optimal control problem of a phase field model for solidification”, Numer. Funct. Anal. and Optimiz., 13:1–2 (1992), 11–27 | DOI | MR | Zbl