RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 2, Pages 199–212 (Mi vuu631)  

MATHEMATICS

The Wallman compactifier and its application for investigation of the abstract attainability problem

E. G. Pytkeevab, A. G. Chentsovab

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia

Abstract: The attainability problem with asymptotic constraints is considered. Such constraints can arise under weakening of constraints that are standard in control theory: phase constraints, boundary and intermediate conditions; trajectories of a system must satisfy these constraints. But asymptotic constraints can arise from the beginning as a characterization of trends in the implementation of desired behavior. For example, one can speak of implementation of powerful control impulses with vanishingly small duration. In this case, it is hard to tell whether any standard constraints are weakened. So, we have a set of complicating conditions with each of which we can juxtapose some analog of the attainability domain in control theory and (more precisely) the image of a subset of the usual solution space under the action of a given operator. In this paper, we investigate questions concerning the structure of an attraction set arising as an analog of the attainability domain. The investigation scheme is based on the application of a special way of extending solution space which admits a natural analogy with Wallman extension used in general topology. Then it is natural to suppose that the space of usual solutions is endowed with a topology (usually, it is a $T_1$-space that is explored in this case). In this connection, questions concerning the replacement of sets forming asymptotic constraints by closures and interiors are addressed. Partially, questions associated with representation of the interior of the set of admissible generalized elements that form an auxiliary attraction set are discussed.

Keywords: asymptotic constraints, extension of a problem, topology.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00505_а
16-01-00649_а


DOI: https://doi.org/10.20537/vm180206

Full text: PDF file (302 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 519.6
MSC: 28A33
Received: 19.03.2018

Citation: E. G. Pytkeev, A. G. Chentsov, “The Wallman compactifier and its application for investigation of the abstract attainability problem”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:2 (2018), 199–212

Citation in format AMSBIB
\Bibitem{PytChe18}
\by E.~G.~Pytkeev, A.~G.~Chentsov
\paper The Wallman compactifier and its application for investigation of the abstract attainability problem
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 2
\pages 199--212
\mathnet{http://mi.mathnet.ru/vuu631}
\crossref{https://doi.org/10.20537/vm180206}
\elib{http://elibrary.ru/item.asp?id=35258687}


Linking options:
  • http://mi.mathnet.ru/eng/vuu631
  • http://mi.mathnet.ru/eng/vuu/v28/i2/p199

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:51
    Full text:23
    References:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019