Geodesic
Transfinite sequences in the method of programmed iterations
Trudy Instituta matematiki i mehaniki, Tome 23 (2017) no. 1, pp. 228-240 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider the problem of retaining the motions of an abstract dynamic system in a given constraint set. Constructions from the method of programmed iterations are extended to problems whose dynamics, in general, does not possess any topological properties. The weaker requirements are compensated by introducing transfinite iterations of the programmed absorption operator. The technique of fixed points of mappings in inductive partially ordered sets is used in the proofs. The proposed procedure produces the set where the problem under consideration is successfully solved in the class of quasistrategies. The control interval is not assumed to be finite.
Keywords: method of programmed iterations, transfinite iterations, quasistrategies, fixed points, inductive posets. 
@article{TIMM_2017_23_1_a22,
     author = {D. A. Serkov},
     title = {Transfinite sequences in the method of programmed iterations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {228--240},
     year = {2017},
     volume = {23},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2017_23_1_a22/}
}
TY  - JOUR
AU  - D. A. Serkov
TI  - Transfinite sequences in the method of programmed iterations
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2017
SP  - 228
EP  - 240
VL  - 23
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2017_23_1_a22/
LA  - ru
ID  - TIMM_2017_23_1_a22
ER  - 
%0 Journal Article
%A D. A. Serkov
%T Transfinite sequences in the method of programmed iterations
%J Trudy Instituta matematiki i mehaniki
%D 2017
%P 228-240
%V 23
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2017_23_1_a22/
%G ru
%F TIMM_2017_23_1_a22
D. A. Serkov. Transfinite sequences in the method of programmed iterations. Trudy Instituta matematiki i mehaniki, Tome 23 (2017) no. 1, pp. 228-240. http://geodesic.mathdoc.fr/item/TIMM_2017_23_1_a22/

[1] Krasovskii N.N., Subbotin A.I., “Alternativa dlya igrovoi zadachi sblizheniya”, Prikl. matematika i mekhanika, 34:6 (1970), 1005–1022

[2] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, Moskva, 1974, 456 pp. | MR

[3] Chentsov A.G., “O strukture odnoi igrovoi zadachi sblizheniya”, Dokl. AN SSSR, 224:6 (1975), 1272–1275 | MR | Zbl

[4] Chentsov A.G., “K igrovoi zadache navedeniya”, Dokl. AN SSSR, 226:1 (1976), 73–76 | MR | Zbl

[5] Ukhobotov V.I., “Postroenie stabilnogo mosta dlya odnogo klassa lineinykh igr”, Prikl. matematika i mekhanika, 41:2 (1977), 358–364 | MR

[6] Chistyakov S.V., “K resheniyu igrovykh zadach presledovaniya”, Prikl. matematika i mekhanika, 41:5 (1977), 825–832 | MR

[7] Ukhobotov V.I., “K postroeniyu stabilnogo mosta v igre uderzhaniya”, Prikl. matematika i mekhanika, 45:2 (1981), 236–240 | MR | Zbl

[8] Dyatlov V.P., Chentsov A.G., “Monotonnye iteratsii mnozhestv i ikh prilozheniya k igrovym zadacham upravleniya”, Kibernetika, 1987, no. 2, 92–99 | Zbl

[9] Chentsov A.G., “Metod programmnykh iteratsii dlya resheniya abstraktnoi zadachi uderzhaniya”, Avtomatika i telemekhanika, 2004, no. 2, 157–169 | Zbl

[10] Chentsov A.G., “O zadache upravleniya s ogranichennym chislom pereklyuchenii”, Deponent VINITI, 1987, 4942-V 87, 1–45, Sverdlovsk

[11] Serkov D.A., Chentsov A.G., “Metod programmnykh iteratsii i operatornaya vypuklost v abstraktnoi zadache uderzhaniya”, Vestn. Udmurt. un-ta. Ser. 1: Matematika. Mekhanika. Kompyuternye nauki, 25:3 (2015), 348–366 | Zbl

[12] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970, 416 pp. | MR

[13] Bourbaki N., “Sur le theoreme de Zorn”, Archiv der Mathematik, 2:6 (1949), 434–437 | DOI | MR

[14] Cousot P., Cousot R., “Constructive versions of Tarski's fixed point theorems”, Pacific J. Math., 82:1 (1979), 43–57 | DOI | MR | Zbl

[15] Echenique F., “A short and constructive proof of Tarski's fixed-point theorem”, Int. J. Game Theory, 33 (2005), 215–218 | DOI | MR | Zbl