Geodesic
Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems
Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 675-687.

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

We obtain lower bounds for the rate of convergence of reconstruction algorithms for distributed-parameter systems of parabolic type. In the case of a pointwise constraint on control for known reconstruction algorithms, we establish a lower bound on the rate of convergence, which shows that, given certain conditions, for each solution of the system one can choose such a collection of measurements so that the reconstruction error will not be less than a certain value. In the case of unbounded controls, we obtain lower bounds for a possible reconstruction error for each trajectory as well as for a given set of trajectories. For a system of special form, we construct an algorithm for which we obtain upper and lower bounds for accuracy having identical order for a specific choice of matching of the parameters. 
@article{MZM_2004_76_5_a3,
     author = {E. V. Vasil'eva},
     title = {Lower {Bounds} for the {Rate} of {Convergence} of {Dynamic} {Reconstruction} {Algorithms} for {Distributed-Parameter} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {675--687},
     publisher = {mathdoc},
     volume = {76},
     number = {5},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a3/}
}
TY  - JOUR
AU  - E. V. Vasil'eva
TI  - Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems
JO  - Matematičeskie zametki
PY  - 2004
SP  - 675
EP  - 687
VL  - 76
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a3/
LA  - ru
ID  - MZM_2004_76_5_a3
ER  - 
%0 Journal Article
%A E. V. Vasil'eva
%T Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems
%J Matematičeskie zametki
%D 2004
%P 675-687
%V 76
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a3/
%G ru
%F MZM_2004_76_5_a3
E. V. Vasil'eva. Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems. Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 675-687. http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a3/

[1] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978

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

[3] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978

[4] Tikhonov A. N., “O funktsionalnykh uravneniyakh Volterra i ikh primeneniyakh k nekotorym zadacham matematicheskoi fiziki”, Byull. Moskovskogo gos. un-ta. (A), T. 1, GONTI, M., 1939

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

[6] Osipov Yu. S., Kryazhimskii A. V., Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, Gordon and Breach, London, 1995 | Zbl

[7] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968

[8] Krasovskii N. N., Subbotin Yu. N., Pozitsionnye differentsialnye igry, Nauka, M., 1984

[9] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, UrO RAN, Ekaterinburg, 2000

[10] Korotkii A. I., Tsepelev I. A., “Verkhnyaya i nizhnyaya otsenki tochnosti v zadache dinamicheskogo opredeleniya operatorov”, Tr. IMM UrO RAN, 4, 227–238 | MR | Zbl

[11] Maksimov V. I., “Ob ustoichivom reshenii obratnykh zadach dlya nelineinykh raspredelennykh sistem. I; II”, Differents. uravneniya, 26:12 (1990), 2059–2067 ; 27:4 (1991), 597–603 | MR | MR | Zbl

[12] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., Zadachi dinamicheskoi regulyarizatsii dlya sistem s raspredelennymi parametrami, Preprint IMM UrO AN SSSR, 1991

[13] Vasileva E. V., Maksimov V. I., “O dinamicheskoi rekonstruktsii neogranichennykh upravlenii v parabolicheskom uravnenii”, Differents. uravneniya, 39:1 (2003), 23–29 | MR

[14] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967