Geodesic
On the reconstruction of inputs in linear parabolic equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 125-135
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The problem of reconstructing distributed inputs in linear parabolic equations is investigated. The algorithm proposed for solving this problem is stable with respect to information disturbances and computational errors. It is based on the combination of methods from the theory of ill-posed problems and from the theory of positional control. The process of reconstructing unknown inputs implemented by the algorithm employs inaccurate measurements of phase coordinates of the system at discrete sufficiently frequent times. In the case when the input is a function of bounded variation, an upper estimate is established for the convergence rate.
Mots-clés : dynamic reconstruction
Keywords: method of controlled models. 
@article{TIMM_2011_17_2_a11,
     author = {V. I. Maksimov},
     title = {On the reconstruction of inputs in linear parabolic equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {125--135},
     year = {2011},
     volume = {17},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a11/}
}
TY  - JOUR
AU  - V. I. Maksimov
TI  - On the reconstruction of inputs in linear parabolic equations
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2011
SP  - 125
EP  - 135
VL  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a11/
LA  - ru
ID  - TIMM_2011_17_2_a11
ER  - 
%0 Journal Article
%A V. I. Maksimov
%T On the reconstruction of inputs in linear parabolic equations
%J Trudy Instituta matematiki i mehaniki
%D 2011
%P 125-135
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a11/
%G ru
%F TIMM_2011_17_2_a11
V. I. Maksimov. On the reconstruction of inputs in linear parabolic equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 125-135. http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a11/

[1] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[2] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979, 286 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 solutions, Gordon and Breach, London, 1995, 625 pp. | MR | Zbl

[5] Maksimov V. I., “Pozitsionnoe modelirovanie neogranichennykh upravlenii dlya nelineinykh sistem s dissipatsiei”, Avtomatika i telemekhanika, 1988, no. 4, 22–30 | MR | Zbl

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

[7] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, Izd-vo UrO RAN, Ekaterinburg, 2000, 305 pp.

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

[9] Kadiev A. M., Maksimov V. I., “Ob odnoi obratnoi zadache dlya parabolicheskogo variatsionnogo neravenstva”, Zhurnal vychisl. matematiki i mat. fiziki, 44:11 (2004), 1983–1992 | MR | Zbl

[10] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972, 310 pp. | MR

[11] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973, 452 pp. | MR

[12] Evans L., Partial Differential Equations, Amer. Math. Soc., Providence, Rhode Island, 1998, 667 pp. | MR

[13] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Moskva, 1965, 520 pp. | MR

[14] Hou L. S., Imanuvilov O., Kwon H. D., “Eigen series solution to terminal-state tracking optimal control problems and exact controllability problems constrained by linear parabolic PDEs”, J. Math. Anal. Appl., 313 (2006), 284–310 | DOI | MR | Zbl