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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2017, Volume 23, Number 1, Pages 228–240
DOI: https://doi.org/10.21538/0134-4889-2017-23-1-228-240 (Mi timm1398) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Transfinite sequences in the method of programmed iterations

D. A. Serkovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (232 kB) Citations (3)
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DOI: https://doi.org/10.21538/0134-4889-2017-23-1-228-240
Abstract: 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.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 31.10.2016
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2018, Volume 300, Issue 1, Pages 153–164
DOI: https://doi.org/10.1134/S0081543818020153
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 37N35, 65J15, 47J25, 52A01, 91A25
Language: Russian
Citation: D. A. Serkov, “Transfinite sequences in the method of programmed iterations”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 1, 2017, 228–240; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 153–164
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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