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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 1, Pages 83–98 (Mi vuu365)  

This article is cited in 7 scientific papers (total in 7 papers)

MATHEMATICS

On controllability of nonlinear distributed systems on a set of discretized controls

A. V. Chernovab

a Nizhni Novgorod State University, Nizhni Novgorod, Russia
b Nizhni Novgorod State Technical University, Nizhni Novgorod, Russia

Abstract: For nonlinear distributed systems representable as a Volterra functional operator equation in a Lebesgue space, sufficient conditions for pointwise controllability with respect to a nonlinear functional are proved. The controls are assumed to belong to a given set $\mathcal D$ of piecewise constant vector functions id est can be regarded as discretized controls. For the equation under study we define the set $\Omega$ of global solvability as the set of all admissible controls for which the equation has a global solution. As an auxiliary result having a separate interest, we also establish under our hypotheses the equality $\Omega=\mathcal D$. The reduction of controlled distributed systems to the functional operator equation under study is illustrated by two examples, namely a Dirichlet boundary value problem for a second order parabolic equation and a mixed boundary value problem for a second order hyperbolic equation; both equations of a rather general form.

Keywords: nonlinear distributed systems, controllability, discretized controls, Volterra functional operator equation.

Full text: PDF file (271 kB)
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UDC: 517.957+517.988+517.977.1
MSC: 47J05, 47J35, 93B05
Received: 25.11.2012

Citation: A. V. Chernov, “On controllability of nonlinear distributed systems on a set of discretized controls”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 1, 83–98

Citation in format AMSBIB
\Bibitem{Che13}
\by A.~V.~Chernov
\paper On controllability of nonlinear distributed systems on a~set of discretized controls
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 1
\pages 83--98
\mathnet{http://mi.mathnet.ru/vuu365}


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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. A. V. Chernov, “Smooth finite-dimensional approximations of distributed optimization problems via control discretization”, Comput. Math. Math. Phys., 53:12 (2013), 1839–1852  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. A. V. Chernov, “O primenimosti tekhniki parametrizatsii upravleniya k resheniyu raspredelennykh zadach optimizatsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 1, 102–117  mathnet
    3. A. V. Chernov, “On convexity local conditions for attainable tubes of controlled distributed systems”, Russian Math. (Iz. VUZ), 58:11 (2014), 60–73  mathnet  crossref
    4. A. V. Chernov, “O kusochno postoyannoi approksimatsii v raspredelennykh zadachakh optimizatsii”, Tr. IMM UrO RAN, 21, no. 1, 2015, 264–279  mathnet  mathscinet  elib
    5. A. V. Chernov, “O totalno globalnoi razreshimosti upravlyaemogo uravneniya tipa Gammershteina s variruemym lineinym operatorom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:2 (2015), 230–243  mathnet  elib
    6. A. V. Chernov, “On a majorant-minorant criterion for the total preservation of global solvability of distributed controlled systems”, Differ. Equ., 52:1 (2016), 111–121  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. A. V. Chernov, “JPEG-like method of control parametrization for numerical solution of the distributed optimization problems”, Autom. Remote Control, 78:8 (2017), 1474–1488  mathnet  crossref  isi  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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