Geodesic
On a modification of the extremal shift method for a second-order differential equation in a Hilbert space
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 150-159 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A problem of tracking a solution of a second-order differential equation in a Hilbert space by a solution of another equation is considered. It is assumed that the first (reference) equation is subject to the action of an unknown control, which is unbounded in time. In the case when the current states of both equation are observed with small errors, a solution algorithm stable with respect to informational noises and computational inaccuracies is designed. The algorithm is based on N.N.Krasovskii's extremal shift method known in the theory of guaranteed control.
Keywords: tracking a solution, extremal shift, second-order equation. 
@article{TIMM_2015_21_2_a11,
     author = {V. I. Maksimov},
     title = {On a modification of the extremal shift method for a second-order differential equation in a {Hilbert} space},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {150--159},
     year = {2015},
     volume = {21},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a11/}
}
TY  - JOUR
AU  - V. I. Maksimov
TI  - On a modification of the extremal shift method for a second-order differential equation in a Hilbert space
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2015
SP  - 150
EP  - 159
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a11/
LA  - ru
ID  - TIMM_2015_21_2_a11
ER  - 
%0 Journal Article
%A V. I. Maksimov
%T On a modification of the extremal shift method for a second-order differential equation in a Hilbert space
%J Trudy Instituta matematiki i mehaniki
%D 2015
%P 150-159
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a11/
%G ru
%F TIMM_2015_21_2_a11
V. I. Maksimov. On a modification of the extremal shift method for a second-order differential equation in a Hilbert space. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 150-159. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a11/

[1] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 458 pp. | MR

[2] Krasovskii N.N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 418 pp. | MR

[3] Osipov Yu.S., Izbrannye trudy, Izd-vo MGU, Moskva, 2009, 656 pp.

[4] Subbotin A.I., Chentsov A.G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 288 pp. | MR

[5] Ushakov V.N., “K zadache postroeniya stabilnykh mostov v differentsialnoi igre sblizheniya-ukloneniya”, Izv. AN SSSR. Tekhnicheskaya kibernetika, 1980, no. 4, 29–36 | MR | Zbl

[6] Barabanova N.N., Subbotin A.I., “O klassakh strategii v differentsialnykh igrakh ukloneniya ot vstrechi”, Prikl. matematika i mekhanika, 35:6 (1971), 345–356 | MR

[7] Patsko V.S., Poverkhnosti pereklyucheniya v lineinykh differentsialnykh igrakh, preprint In-t matematiki i mekhaniki UrO RAN, 2004, 80 pp.

[8] Maksimov V.I., “Ob otslezhivanii traektorii dinamicheskoi sistemy”, Prikl. matematika i mekhanika, 75:6 (2011), 951–960 | MR | Zbl

[9] Maksimov V.I., “Ob otslezhivanii resheniya parabolicheskogo uravneniya”, Izv. vuzov. Matematika, 2012, no. 1, 1–9 | Zbl

[10] Kryazhimskii A.V., Maksimov V.I., “Zadacha resursosberegayuschego slezheniya na beskonechnom promezhutke vremeni”, Differents. uravneniya, 47:7 (2011), 993–1002 | MR

[11] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978, 336 pp. | MR

[12] Osipov Yu.S., Vasilev F.P., Potapov M.M., Osnovy metoda dinamicheskoi regulyarizatsii, Izd-vo MGU, M., 1999, 237 pp.

[13] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp. | MR