Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
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


Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, Volume 28, Issue 4, Pages 489–512
DOI: https://doi.org/10.20537/vm180405
(Mi vuu653)
 

MATHEMATICS

On reducing the motion of a controlled system to a Lebesgue set of a Lipschitz function

V. N. Ushakovab, A. A. Ershovba, G. V. Parshikova

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
References:
Abstract: We consider a nonlinear controlled system in a finite-dimensional Euclidean space defined on a finite time interval. One of the main problems of mathematical control theory is studied: the problem of approaching a phase vector of a controlled system with a compact target set in the phase space at a fixed time instant. In this paper, a Lebesgue set of a scalar Lipschitz function defined on the phase space is a target set. The mentioned approach problem is closely connected with many important and key problems of control theory and, in particular, with the problem of optimally reducing a controlled system to a target set. Due to the complexity of the approach problem for nontrivial controlled systems, an analytical representation of solutions is impossible even for relatively simple controlled systems. Therefore, in the present work, we study first of all the issues related to the construction of an approximate solution of the approach problem. The construction of an approximate solution by the method described in the paper is primarily concerned with the design of the integral funnel of the controlled system, presented in the so-called “reverse” time. To date, there are several algorithms for constructing a resolving program control in the approach problem. This paper presents an algorithm for constructing a control based on the maximum attraction of the system's motion to the solvability set of the approach problem. Examples are provided.
Keywords: control system, Lebesgue set, solvability set, optimal control.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Russian Foundation for Basic Research 18-01-00221_а
18-01-00264_а
The work was supported by Act 211 of the Government of the Russian Federation, contract no. 02.A03.21.0006. The studies of the first and second authors were supported by the Russian Foundation for Basic Research (project no. 18-01-00221). The study of the third author was supported by the Russian Foundation for Basic Research (project no. 18-01-00264).
Received: 13.10.2018
Bibliographic databases:
Document Type: Article
UDC: 517.977.58
MSC: 49M25
Language: Russian
Citation: V. N. Ushakov, A. A. Ershov, G. V. Parshikov, “On reducing the motion of a controlled system to a Lebesgue set of a Lipschitz function”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:4 (2018), 489–512
Citation in format AMSBIB
\Bibitem{UshErsPar18}
\by V.~N.~Ushakov, A.~A.~Ershov, G.~V.~Parshikov
\paper On reducing the motion of a controlled system to a Lebesgue set of a Lipschitz function
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 4
\pages 489--512
\mathnet{http://mi.mathnet.ru/vuu653}
\crossref{https://doi.org/10.20537/vm180405}
\elib{https://elibrary.ru/item.asp?id=36873366}
Linking options:
  • https://www.mathnet.ru/eng/vuu653
  • https://www.mathnet.ru/eng/vuu/v28/i4/p489
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Statistics & downloads:
    Abstract page:400
    Full-text PDF :385
    References:33
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024