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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 2, Pages 68–87 (Mi vuu217)  

This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

The statistically invariant sets of controllable systems with random parameters

L. I. Rodina

Udmurt State University, Izhevsk, Russia

Abstract: We investigate the properties of statistical invariance and statistically weak invariance with probability one for control systems with random parameters. We obtain the sufficient conditions for the invariance of the given set with respect to the control system formulated in terms of Lyapunov functions and the dynamical system of shifts. We prove the extension for the theorem of S. A. Chaplygin about differential inequalities and obtain the conditions of existence for the upper solution of Cauchy problem with piecewise continuous on $t$ right-hand part without assumption of uniqueness of solution.

Keywords: controllable systems, dynamical systems, differential inclusions, statistically invariant sets with probability one.

Full text: PDF file (277 kB)
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UDC: 517.935+517.938
MSC: 34A60, 37N35, 49J15, 93B03
Received: 25.12.2010

Citation: L. I. Rodina, “The statistically invariant sets of controllable systems with random parameters”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 2, 68–87

Citation in format AMSBIB
\Bibitem{Rod11}
\by L.~I.~Rodina
\paper The statistically invariant sets of controllable systems with random parameters
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 2
\pages 68--87
\mathnet{http://mi.mathnet.ru/vuu217}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. L. I. Rodina, “Statisticheskie kharakteristiki mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2012, no. 1(39), 111–113  mathnet
    3. L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164  mathnet
    4. 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
    5. L. I. Rodina, “Estimation of statistical characteristics of attainability sets of controllable systems”, Russian Math. (Iz. VUZ), 57:11 (2013), 17–27  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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