Geodesic
On a dynamic game problem with an indecomposable set of disturbances
Ural mathematical journal, Tome 5 (2019) no. 2, pp. 72-79 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For an abstract dynamic system, a game problem of retention of the motions in a given set of the motion histories is considered. The case of an indecomposable set of disturbances is studied. The set of successful solvability and a construction of a resolving quasistrategy based on the method of programmed iterations is proposed.
Keywords: Indecomposable disturbances, Quasistrategy, Retention problem. 
@article{UMJ_2019_5_2_a6,
     author = {Dmitriy A. Serkov},
     title = {On a dynamic game problem with an indecomposable set of disturbances},
     journal = {Ural mathematical journal},
     pages = {72--79},
     year = {2019},
     volume = {5},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2019_5_2_a6/}
}
TY  - JOUR
AU  - Dmitriy A. Serkov
TI  - On a dynamic game problem with an indecomposable set of disturbances
JO  - Ural mathematical journal
PY  - 2019
SP  - 72
EP  - 79
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UMJ_2019_5_2_a6/
LA  - en
ID  - UMJ_2019_5_2_a6
ER  - 
%0 Journal Article
%A Dmitriy A. Serkov
%T On a dynamic game problem with an indecomposable set of disturbances
%J Ural mathematical journal
%D 2019
%P 72-79
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/UMJ_2019_5_2_a6/
%G en
%F UMJ_2019_5_2_a6
Dmitriy A. Serkov. On a dynamic game problem with an indecomposable set of disturbances. Ural mathematical journal, Tome 5 (2019) no. 2, pp. 72-79. http://geodesic.mathdoc.fr/item/UMJ_2019_5_2_a6/

[1] Chentsov A. G., “On a game problem of converging at a given instant of time”, Math. USSR-Sb., 28:3 (1976), 353–376 | DOI | MR

[2] Chentsov A. G., “On a game problem of guidance with information memory”, Dokl. Akad. Nauk SSSR, 227:2 (1976), 306–309 (in Russian) | MR

[3] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Panstwowe Wydawnictwo Naukowe, Warszawa, 1985, 540 pp.

[4] Gomoyunov M. I., Serkov D., “Control with a guide in the guarantee optimization problem under functional constraints on the disturbance”, Proc. Steklov Inst. Math., 299, Suppl. 1 (2017), S49–S60 | DOI | MR | Zbl

[5] Krasovskii N. N., Subbotin A. I., Game-Theoretical Control Problems, Springer-Verlag, New York, 1988, 517 pp. | MR | Zbl

[6] Ledyaev Y. S., “Program-predictive feedback control for systems with evolving dynamics”, IFAC-PapersOnLine, 51:32 (2018), 723—726 | DOI

[7] Rockafellar R. T., “Integrals which are convex functionals”, Pacific J. Math., 24:3, 525–539 | DOI | MR | Zbl

[8] Serkov D. A., “Transfinite sequences in the programmed iteration method.”, Proc. Steklov Inst. Math., 300, Suppl. 1, S153–S164 | DOI | MR | Zbl

[9] Serkov D. A., Chentsov A. G., “The elements of the operator convexity in the construction of the programmed iteration method”, Bull. South Ural State Univ. Ser. Math. Modell. Program. Comp. Software, 9:3 (2016), 82–93 | DOI | MR | Zbl