Geodesic
On the optimal control for the elastic plate's vibrations in the conflict situations
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2004), pp. 33-38.

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

It is discussed the problem of an optimal control for the plate's linear vibrations, when the distributive disposed forces influence on it. The problem is solved by the method of Fourie and it is brought to the differential game, which is described by the infinitesimal differential equations of second order. The extremal strategies are constructed by the extreme targeting method. It is shown that if the resources of the first player are more than the resources of the second player and the influencing forces belong to class $L_2$, then the problem of damping of plate's vibrations is solved. In the end of the article a numerical example is given.
Keywords: Plate's linear vibrations, extreme targeting method. 
@article{UZERU_2004_2_a4,
     author = {L. A. Mazmanyan},
     title = {On the optimal control for the elastic plate's  vibrations in the conflict situations},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {33--38},
     publisher = {mathdoc},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2004_2_a4/}
}
TY  - JOUR
AU  - L. A. Mazmanyan
TI  - On the optimal control for the elastic plate's  vibrations in the conflict situations
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2004
SP  - 33
EP  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2004_2_a4/
LA  - ru
ID  - UZERU_2004_2_a4
ER  - 
%0 Journal Article
%A L. A. Mazmanyan
%T On the optimal control for the elastic plate's  vibrations in the conflict situations
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2004
%P 33-38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2004_2_a4/
%G ru
%F UZERU_2004_2_a4
L. A. Mazmanyan. On the optimal control for the elastic plate's  vibrations in the conflict situations. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2004), pp. 33-38. http://geodesic.mathdoc.fr/item/UZERU_2004_2_a4/

[1] A. S. Volmir, Nelineinaya dinamika plastinok i oboloche, M., Nauka, 1972

[2] L. A. Mazmanyan, “Ob optimalnom upravlenii lineinykh kolebanii plastinki v konfliktnykh situatsiyakh”, Optimalnoe upravlenie, ustoichivost i prochnost mekhanicheskikh sistem, Er., 2002, 48—52

[3] M. S. Gabrielyan, Izv. NAN RA, Mekhanika, 1998, no. 4, 72—76 | MR

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