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


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 1, Pages 67–86 (Mi vuu208)  

This article is cited in 12 scientific papers (total in 12 papers)

MATHEMATICS

The statistically weak invariant sets of control systems

L. I. Rodinaa, E. L. Tonkovb

a Udmurt State University, Izhevsk, Russia
b Udmurt State University, Izhevsk, Russia

Abstract: We obtain the conditions that allow to estimate the relative frequency of occurrence of the attainable set of a control system in some given set. The set is called statistically invariant if the relative frequency of occurrence in this set is equal to one. We also derive the conditions of the statistically weak invariance of the given set with respect to controllable system, that is, for every initial point from this set, at least one solution of the control system is statistically invariant. We suggest that the images of the right hand part of the differential inclusions corresponding for the given control system are closed but may be not compact. The main results are formulated in the terms of Lyapunov functions, metric of Hausdorff–Bebutov and the dynamical system of shifts that attended in the right hand part of the differential inclusion.

Keywords: controllable systems, dynamical systems, differential inclusions, weakly invariant and statistically weakly invariant sets.

Full text: PDF file (278 kB)
References: PDF file   HTML file
UDC: 517.935+517.938
MSC: 34A60, 37N35, 49J15, 93B03
Received: 10.10.2010

Citation: L. I. Rodina, E. L. Tonkov, “The statistically weak invariant sets of control systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 1, 67–86

Citation in format AMSBIB
\Bibitem{RodTon11}
\by L.~I.~Rodina, E.~L.~Tonkov
\paper The statistically weak invariant sets of control systems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 1
\pages 67--86
\mathnet{http://mi.mathnet.ru/vuu208}


Linking options:
  • http://mi.mathnet.ru/eng/vuu208
  • http://mi.mathnet.ru/eng/vuu/y2011/i1/p67

    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

    This publication is cited in the following articles:
    1. L. I. Rodina, “Statisticheski invariantnye mnozhestva upravlyaemykh sistem so sluchainymi parametrami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 2, 68–87  mathnet
    2. L. I. Rodina, “Statisticheskie kharakteristiki mnozhestva dostizhimosti i periodicheskie protsessy upravlyaemykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 2, 34–43  mathnet
    3. L. I. Rodina, “Statisticheskie kharakteristiki mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2012, no. 1(39), 111–113  mathnet
    4. L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164  mathnet
    5. L. I. Rodina, “The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff–Bebutov metric and statistically invariant sets of control systems”, Proc. Steklov Inst. Math., 278 (2012), 208–217  mathnet  crossref  mathscinet  isi  elib  elib
    6. L. I. Rodina, E. L. Tonkov, “O mnozhestve dostizhimosti upravlyaemoi sistemy bez predpolozheniya kompaktnosti geometricheskikh ogranichenii na dopustimye upravleniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 68–79  mathnet
    7. L. I. Rodina, A. Kh. Khammadi, “Kharakteristiki mnozhestva dostizhimosti, svyazannye s invariantnostyu upravlyaemoi sistemy na konechnom promezhutke vremeni”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 35–48  mathnet
    8. L. I. Rodina, “Estimation of statistical characteristics of attainability sets of controllable systems”, Russian Math. (Iz. VUZ), 57:11 (2013), 17–27  mathnet  crossref
    9. Ya. Yu. Larina, L. I. Rodina, “Statisticheskie kharakteristiki upravlyaemykh sistem, voznikayuschie v razlichnykh modelyakh estestvoznaniya”, Model. i analiz inform. sistem, 20:5 (2013), 62–77  mathnet
    10. A. Kh. Khammadi, “Kharakteristiki invariantnosti mnozhestva dostizhimosti upravlyaemykh sistem so sluchainymi koeffitsientami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 100–110  mathnet
    11. L. I. Rodina, A. Kh. Khammadi, “Statistical characteristics of attainability set of controllable systems with random coefficients”, Russian Math. (Iz. VUZ), 58:11 (2014), 43–53  mathnet  crossref
    12. Ya. Yu. Larina, L. I. Rodina, “Statistical characteristics of continuous functions and statistically weakly invariant sets of controllable system”, Russian Math. (Iz. VUZ), 61:2 (2017), 28–35  mathnet  crossref  isi
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:440
    Full text:160
    References:39
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020