Geodesic
On tracking solutions of parabolic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 40-48.

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

We consider a control problem for a parabolic equation. It consists in constructing an algorithm for finding a feedback control such that a solution of a given equation should track a solution of another equation generated by an unknown right-hand side. We propose two noise-resistant solution algorithms for the indicated problem. They are based on the extremal shift method well-known in the guaranteed control theory. The first algorithm is applicable in the case of “continuous” measuring of phase states, whereas the second one implies discrete measuring.
Keywords: systems with distributed parameters, control. 
@article{IVM_2012_1_a4,
     author = {V. I. Maksimov},
     title = {On tracking solutions of parabolic equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {40--48},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_1_a4/}
}
TY  - JOUR
AU  - V. I. Maksimov
TI  - On tracking solutions of parabolic equations
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2012
SP  - 40
EP  - 48
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2012_1_a4/
LA  - ru
ID  - IVM_2012_1_a4
ER  - 
%0 Journal Article
%A V. I. Maksimov
%T On tracking solutions of parabolic equations
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2012
%P 40-48
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2012_1_a4/
%G ru
%F IVM_2012_1_a4
V. I. Maksimov. On tracking solutions of parabolic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 40-48. http://geodesic.mathdoc.fr/item/IVM_2012_1_a4/

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

[2] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR | Zbl

[3] Bensoussan A., Da Prato G., Delfour M., Mitter S., Representation and control of infinite dimensional systems, Birkhäuser, Boston–Basel–Berlin, 1992 | Zbl

[4] Barbu V., Optimal control of variational inequalities, Pitman Advanced Publishing Program, London, 1984 | MR | Zbl

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

[6] Vaisburd I. F., Osipov Yu. S., “Differentsialnaya igra sblizheniya dlya sistem s raspredelennymi parametrami”, PMM, 39:5 (1975), 772–779 | MR

[7] Kryazhimskii A. V., Osipov Yu. S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Tekhnich. kibernetika, 1983, no. 2, 51–68 | MR

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

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

[10] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl