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Avtomat. i Telemekh., 2013, Issue 12, Pages 56–103 (Mi at6171)  

This article is cited in 18 scientific papers (total in 18 papers)

Topical issue

Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations

B. M. Millerab, E. Ya. Rubinovichc

a Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia
b School of Mathematical Sciences, Monash University, Victoria, Australia
c Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: Consideration was given to the problems of variational calculus and optimal control admitting impulsive controls and, correspondingly, discontinuous solutions. The evolution of the notion of singular space-time transformation beginning from the problem of classical variational calculus and ending with the problems of optimal control at the phase of impact was shown.

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English version:
Automation and Remote Control, 2013, 74:12, 1969–2006

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Presented by the member of Editorial Board: . . 

Received: 04.02.2013

Citation: B. M. Miller, E. Ya. Rubinovich, “Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations”, Avtomat. i Telemekh., 2013, no. 12, 56–103; Autom. Remote Control, 74:12 (2013), 1969–2006

Citation in format AMSBIB
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\by B.~M.~Miller, E.~Ya.~Rubinovich
\paper Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations
\jour Avtomat. i Telemekh.
\yr 2013
\issue 12
\pages 56--103
\mathnet{http://mi.mathnet.ru/at6171}
\transl
\jour Autom. Remote Control
\yr 2013
\vol 74
\issue 12
\pages 1969--2006
\crossref{https://doi.org/10.1134/S0005117913120047}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84891548996}


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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. A. A. Galyaev, “On the mathematical model of one-dimensional impact of a chain of viscoelastic bodies”, Autom. Remote Control, 76:10 (2015), 1743–1750  mathnet  crossref  isi  elib  elib
    2. A. N. Sesekin, N. I. Zhelonkina, “Stability of nonlinear dynamical systems containing the product of discontinuous functions and distributions”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040011  crossref  isi  scopus
    3. A. N. Sesekin, I. Yu. Andreeva, A. S. Shlyakhov, “Singular linear quadratic control problem for systems with linear and constant delay”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conf. Proc., 1789, ed. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040010  crossref  isi  scopus
    4. B. M. Miller, E. Ya. Rubinovich, “Dinamicheskie sistemy s razryvnymi resheniyami i zadachi s neogranichennymi proizvodnymi”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 136–149  mathnet  crossref
    5. 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
    6. T. K. Yuldashev, “Nelineinoe optimalnoe upravlenie v obratnoi zadache dlya odnoi sistemy s parabolicheskim uravneniem”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2017, no. 2, 59–78  mathnet  crossref  elib
    7. A. A. Galyaev, P. V. Lysenko, “Zadacha optimalnogo bystrodeistviya pri uprugom i vyazkouprugom vzaimodeistviyakh tela s poverkhnostyu”, Probl. upravl., 4 (2018), 14–20  mathnet  crossref
    8. V. A. Dykhta, O. N. Samsonyuk, “Pozitsionnyi printsip minimuma dlya impulsnykh protsessov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 25 (2018), 46–62  mathnet  crossref
    9. M. Motta, “Minimum time problem with impulsive and ordinary controls”, Discret. Contin. Dyn. Syst., 38:11 (2018), 5781–5809  crossref  mathscinet  zmath  isi  scopus
    10. O. N. Samsonyuk, S. A. Timoshin, “Bv solutions of rate independent processes driven by impulsive controls”, IFAC-PapersOnLine, 51:32 (2018), 361–366  crossref  isi  scopus
    11. V. A. Dykhta, O. N. Samsonyuk, “Optimality conditions with feedback controls for optimal impulsive control problems”, IFAC-PapersOnLine, 51:32 (2018), 509–514  crossref  isi  scopus
    12. O. N. Samsonyuk, M. V. Staritsyn, “Rough paths theory and impulsive control: a promising connection”, IFAC-PapersOnLine, 51:32 (2018), 615–618  crossref  isi  scopus
    13. Goncharova E., Staritsyn M., “On Connection Between Two Conventional Types of Impulsive Control Systems in Respect of Sensitivity and Relaxation”, 2018 European Control Conference (Ecc), IEEE, 2018, 460–465  isi
    14. N. I. Zhelonkina, A. N. Sesekin, “Ob ustoichivosti reshenii nelineinykh sistem s impulsnoi strukturoi”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:124 (2018), 624–636  mathnet  crossref  elib
    15. Samsonyuk O.N., Timoshin S.A., “Optimal Control Problems With States of Bounded Variation and Hysteresis”, J. Glob. Optim., 74:3 (2019), 565–596  crossref  isi
    16. B. M. Miller, E. Ya. Rubinovich, “Numerical analysis of shock interactions with the example of Painleve paradox with a “slanted” fall of a rod”, Autom. Remote Control, 80:10 (2019), 1835–1846  mathnet  crossref  crossref  isi  elib
    17. T. K. Yuldashev, “Ob odnom optimalnom upravlenii obratnymi teplovymi protsessami s integralnym usloviem pereopredeleniya”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2019, no. 4, 65–87  mathnet  crossref  elib
    18. A. N. Sesekin, N. I. Zhelonkina, “On the stability of tubes of discontinuous solutions of bilinear systems with delay”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 31 (2020), 96–110  mathnet  crossref
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