Infinite-horizon stable control of a parabolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1503-1510 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The control of a parabolic equation is considered. The solution of this equation is assumed to be measured inaccurately. An algorithm is described for finding a feedback control function such that the solution of this equation tracks the solution of another equation generated by an unknown right-hand side.
@article{ZVMMF_2015_55_9_a5,
     author = {M. S. Blizorukova},
     title = {Infinite-horizon stable control of a parabolic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1503--1510},
     year = {2015},
     volume = {55},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a5/}
}
TY  - JOUR
AU  - M. S. Blizorukova
TI  - Infinite-horizon stable control of a parabolic equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1503
EP  - 1510
VL  - 55
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a5/
LA  - ru
ID  - ZVMMF_2015_55_9_a5
ER  - 
%0 Journal Article
%A M. S. Blizorukova
%T Infinite-horizon stable control of a parabolic equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1503-1510
%V 55
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a5/
%G ru
%F ZVMMF_2015_55_9_a5
M. S. Blizorukova. Infinite-horizon stable control of a parabolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1503-1510. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a5/

[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

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

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

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

[6] Osipov Yu. S., “Pozitsionnoe upravlenie v parabolicheskikh sistemakh”, Prikl. matem. i mekhan., 41:2 (1977), 195–201 | MR

[7] Osipov Yu. S., Izbrannye trudy, MGU, M., 2009

[8] Maksimov V. I., “Ob otslezhivanii resheniya parabolicheskogo uravneniya”, Izv. vyssh. uchebn. zavedenii. Matematika, 2012, no. 1, 40–48 | MR

[9] Maksimov V. I., “Regularized extremal shift in problems of stable control”, System modeling and optimization, IFIP AICT, 391, eds. D. Homberg, F. Troltzsch, CSMO, 2013, 112–121 | Zbl

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

[11] Osipov Yu. S., Vasilev F. P., Potapov M. M., Osnovy metoda dinamicheskoi regulyarizatsii, Izd-vo MGU, M., 1999

[12] Kryazhimskii A. V., Maksimov V. I., “Resource-saving infinite-horizon tracing under uncertain input”, Appl. Math. and Computation, 217 (2010), 1135–1140 | DOI | MR

[13] Kryazhimskii A. V., Maksimov V. I., “Zadachi resursosberegayuschego slezheniya na beskonechnom promezhutke vremeni”, Differents. ur-niya, 47:7 (2011), 993–1002 | MR | Zbl