Geodesic
On the problem of synthesis of piece-wise mixed-type strategies
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1991), pp. 28-39 
V. K. Stepanyan. On the problem of synthesis of piece-wise mixed-type strategies. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1991), pp. 28-39. http://geodesic.mathdoc.fr/item/UZERU_1991_2_a4/
@article{UZERU_1991_2_a4,
     author = {V. K. Stepanyan},
     title = {On the problem of synthesis of piece-wise mixed-type strategies},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {28--39},
     year = {1991},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_1991_2_a4/}
}
TY  - JOUR
AU  - V. K. Stepanyan
TI  - On the problem of synthesis of piece-wise mixed-type strategies
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 1991
SP  - 28
EP  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UZERU_1991_2_a4/
LA  - ru
ID  - UZERU_1991_2_a4
ER  - 
%0 Journal Article
%A V. K. Stepanyan
%T On the problem of synthesis of piece-wise mixed-type strategies
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 1991
%P 28-39
%N 2
%U http://geodesic.mathdoc.fr/item/UZERU_1991_2_a4/
%G ru
%F UZERU_1991_2_a4

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

A method of building piece-wise mixed-type strategies is studied in differential games by means of stochastic programming synthesis for non-linear systems. It is proved that the introduction of the auxiliary phase coordinate makes possible to build rationally such a function, which approximates the value of the game and is differentiable on all phase coordinates. In this case the optimal strategy is defined through the condition that the extremal replacement must be opposite to the gradient of the approximation function.

[1] V. K. Stepanyan, “Ob odnoi differentsialnoi igre v klasse kusochno-smeshanykh strategii”, Mekhannka (mezhvuz. sb), 1990, no. 8

[2] N. N. Krasovskii, Upravlenie dinamicheskimi sistemami, Nauka, M., 1985 | MR

[3] A. N. Shiryaev, Veroyatnost, Nauka, M., 1980 | MR | Zbl

[4] M. Loev, Teoriya veroyatnostei, Izd-vo inostr. lit-ry, M., 1962 | MR | Zbl

[5] Yu. A. Rozanov, Sluchainye protsessy, Nauka, M., 1971 | MR | Zbl

[6] Krasovskii N. N., Subbotin A. N., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR

[7] M. S. Gabrielyan, Differentsialnye igry pri $m$ tselevykh mnozhestvakh, Avtoreferat na soisk. uch. st. doktora fiz.-mat. nauk, EGU, Er., 1986

[8] A. N. Krasovskii, Sintez smeshannykh strategii upravleniya, UrGU, Sverdlovsk, 1988, 151 pp.

[9] V. E. Tretyakov, “Sintez optimalnogo garantiruyuschego upravleniya”, Protsessy upravleniya i teorii informatsii, 17:4 (1988) | Zbl