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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 1, Pages 162–177 (Mi timm680)  

This article is cited in 14 scientific papers (total in 14 papers)

The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff–Bebutov metric and differential inclusions

E. A. Panasenkoa, L. I. Rodinab, E. L. Tonkovb

a Tambov State University
b Udmurt State University

Abstract: The paper is devoted to studying the space of nonempty closed convex (but not necessarily compact) sets in $\mathbb R^n$, a dynamical system of translations, and existence theorems for differential inclusions. This space is made complete by equipping it with the Hausdorff–Bebutov metric. The investigation of these issues is important for certain problems of optimal control of asymptotic characteristics of the controlled system. For example, the problem $\dot x=A(t,u)x$, $(u,x)\in\mathbb R^{m+n}$, $\lambda_n(u(\cdot))\to\min$, where $\lambda_n(u(\cdot))$ – is the maximal Lyapunov exponent of the system $\dot x=A(t,u)x$, leads to a differential inclusion with a noncompact right-hand side.

Keywords: Hausdorff–Bebutov metric, control systems, differential inclusions, dynamical system of translations.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 275, suppl. 1, S121–S136

Bibliographic databases:

UDC: 517.977
Received: 31.07.2010

Citation: E. A. Panasenko, L. I. Rodina, E. L. Tonkov, “The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff–Bebutov metric and differential inclusions”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 1, 2011, 162–177; Proc. Steklov Inst. Math. (Suppl.), 275, suppl. 1 (2011), S121–S136

Citation in format AMSBIB
\by E.~A.~Panasenko, L.~I.~Rodina, E.~L.~Tonkov
\paper The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff--Bebutov metric and differential inclusions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 1
\pages 162--177
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 275
\issue , suppl. 1
\pages S121--S136

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    This publication is cited in the following articles:
    1. E. S. Zhukovskii, E. A. Panasenko, “Ob odnoi metrike v prostranstve nepustykh zamknutykh podmnozhestv prostranstva $\mathbb R^n$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 1, 15–25  mathnet
    2. E. A. Panasenko, “Dinamicheskaya sistema sdvigov v prostranstve mnogoznachnykh funktsii s zamknutymi obrazami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 2, 28–33  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. E. S. Zhukovskiy, E. A. Panasenko, “On fixed points of multi-valued maps in metric spaces and differential inclusions”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 2, 12–26  mathnet
    9. E. L. Tonkov, “Magistralnye protsessy upravlyaemykh sistem na gladkikh mnogoobraziyakh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 132–145  mathnet
    10. Zhukovskiy E.S., Panasenko E.A., “On Multi-Valued Maps with Images in the Space of Closed Subsets of a Metric Space”, Fixed Point Theory Appl., 2013, 10  crossref  mathscinet  zmath  isi  elib  scopus
    11. P. D. Lebedev, V. N. Ushakov, “Ob odnom variante metriki dlya neogranichennykh vypuklykh mnozhestv”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 5:1 (2013), 40–49  mathnet
    12. E. L. Tonkov, “Barbashin and Krasovskii's asymptotic stability theorem in application to control systems on smooth manifolds”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 208–221  mathnet  crossref  mathscinet  isi  elib
    13. A. A. Tolstonogov, “Prostranstvo nepreryvnykh mnogoznachnykh otobrazhenii s zamknutymi neogranichennymi znacheniyami”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 200–208  mathnet  crossref  elib
    14. L. I. Danilov, “Shift dynamical systems and measurable selectors of multivalued maps”, Sb. Math., 209:11 (2018), 1611–1643  mathnet  crossref  crossref  adsnasa  isi  elib
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