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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 2, Pages 34–43 (Mi vuu320)  

This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

Statistical characteristics of attainability set and periodic processes of control systems

L. I. Rodina

Department of Mathematical Analysis, Udmurt State University, Izhevsk, Russia

Abstract: We investigate the statistical characteristics of attainability set $A(t,\sigma,X)$ of control system
\begin{equation} \dot x=f(h^t\sigma,x,u),\quad(t,\sigma,x,u)\in\mathbb R\times\Sigma\times\mathbb R^n\times\mathbb R^m, \tag{1} \end{equation}
which is parametrized by means of topological dynamic system $(\Sigma,h^t)$. We obtained the lower estimations for such characteristics as the relative frequency of containing, the upper and lower relative frequencies of containing of attainability set of the system (1) in the given set $M$ as well as new sufficient conditions of statistical invariance of the set $M$ with respect to control system. We received the conditions for system (1) and set $X$ at which for given $\sigma\in\Sigma$ and $\varkappa_0\in (0,1]$ the relative frequency of containing of attainability set $A(t,\sigma,X)$ of systems (1) in the set $M$ not less $\varkappa_0$. Results of the work are illustrated by the example of control system which describes periodic processes in a chemical reactor.

Keywords: controll systems, dynamical systems, differential inclusions, statistically invariant sets.

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UDC: 517.935+517.938
MSC: 34A60, 37N35, 49J15, 93B03
Received: 30.03.2012

Citation: L. I. Rodina, “Statistical characteristics of attainability set and periodic processes of control systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 2, 34–43

Citation in format AMSBIB
\Bibitem{Rod12}
\by L.~I.~Rodina
\paper Statistical characteristics of attainability set and periodic processes of control systems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 2
\pages 34--43
\mathnet{http://mi.mathnet.ru/vuu320}


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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, 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
    2. L. I. Rodina, “Estimation of statistical characteristics of attainability sets of controllable systems”, Russian Math. (Iz. VUZ), 57:11 (2013), 17–27  mathnet  crossref
    3. 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
    4. A. Kh. Khammadi, “O svoistvakh kharakteristik mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2015, no. 2(46), 216–227  mathnet  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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