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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 4, Pages 262–269 (Mi timm442)  

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

Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control

T. F. Filippova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A method of constructing ellipsoidal estimates of reachable sets is proposed for a nonlinear system with a scalar impulsive control and uncertainty in initial data. A special discontinuous change of time is used to transform the impulsive system under consideration into an ordinary differential inclusion without impulsive components. To estimate reachable sets of the obtained nonlinear differential inclusion, results from the theory of ellipsoidal estimation and theory of evolution equations of set-valued states of dynamical systems under uncertainty are used.

Keywords: reachable set, impulsive control, trajectory tubes, set-valued estimates, differential inclusions.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 269, suppl. 1, S95–S102

Document Type: Article
UDC: 517.977
Received: 20.05.2009

Citation: T. F. Filippova, “Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 262–269; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S95–S102

Citation in format AMSBIB
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\by T.~F.~Filippova
\paper Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 262--269
\mathnet{http://mi.mathnet.ru/timm442}
\elib{http://elibrary.ru/item.asp?id=12952771}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S95--S102
\crossref{https://doi.org/10.1134/S008154381006009X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962476802}


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    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. T. F. Filippova, “Differential equations of ellipsoidal estimates for reachable sets of a nonlinear dynamical control system”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S75–S84  mathnet  crossref  isi  elib
    2. N. I. Zhelonkina, A. N. Sesekin, S. P. Sorokin, “Ob ustoichivosti lineinykh sistem s impulsnym vozdeistviem v matritse sistemy i zapazdyvaniem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 1, 40–46  mathnet
    3. T. F. Filippova, O. G. Matviichuk, “Algorithms to estimate the reachability sets of the pulse controlled systems with ellipsoidal phase constraints”, Autom. Remote Control, 72:9 (2011), 1911–1924  mathnet  crossref  mathscinet  zmath  isi
    4. V. N. Ushakov, A. R. Matviichuk, A. V. Ushakov, “Approksimatsiya mnozhestv dostizhimosti i integralnykh voronok differentsialnykh vklyuchenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 23–39  mathnet
    5. A. V. Ushakov, “Ob odnom variante priblizhennogo postroeniya razreshayuschikh upravlenii v zadache o sblizhenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 94–107  mathnet
    6. T. F. Filippova, “Estimates of reachable sets of control systems with nonlinearity and parametric perturbations”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 67–75  mathnet  crossref  mathscinet  isi  elib
    7. V. N. Ushakov, A. R. Matviichuk, “K resheniyu zadach upravleniya nelineinymi sistemami na konechnom promezhutke vremeni”, Izv. IMI UdGU, 2015, no. 2(46), 202–215  mathnet  elib
    8. O. N. Samsonyuk, M. V. Staritsyn, “Impulsnye upravlyaemye sistemy s traektoriyami ogranichennoi $p$-variatsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 164–177  mathnet  crossref
    9. T. F. Filippova, “Otsenki mnozhestv dostizhimosti sistem s impulsnym upravleniem, neopredelennostyu i nelineinostyu”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 205–216  mathnet  crossref
    10. G. V. Parshikov, “O priblizhennom vychislenii mnozhestva razreshimosti v zadache o sblizhenii statsionarnoi upravlyaemoi sistemy na konechnom promezhutke vremeni”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 210–221  mathnet  crossref  elib
    11. Matviychuk A.R., Ukhobotov V.I., Ushakov A.V., Ushakov V.N., “The Approach Problem of a Nonlinear Controlled System in a Finite Time Interval”, Pmm-J. Appl. Math. Mech., 81:2 (2017), 114–128  crossref  mathscinet  isi  scopus
    12. V. A. Dykhta, O. N. Samsonyuk, “Pozitsionnyi printsip minimuma dlya impulsnykh protsessov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 25 (2018), 46–62  mathnet  crossref
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