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Avtomat. i Telemekh., 2009, Issue 4, Pages 18–30 (Mi at447)  

This article is cited in 17 scientific papers (total in 17 papers)

Systems with Distributed Parameters

N. N. Krasovskii's extremal shift method and problems of boundary control

Yu. S. Osipova, A. V. Kryazhimskiib, V. I. Maksimovc

a Presidium of the Russian Academy of Sciences, Moscow, Russia
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
c Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

Abstract: For the boundary-controlled dynamic system obeying a parabolic differential equation with the Neumann boundary condition, the problems of following the reference motion, following the reference control, and guaranteed control (at domination of the controller resource) were solved on the basis of the N. N. Krasovskii method of extremal shift from the theory of positional differential games.

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English version:
Automation and Remote Control, 2009, 70:4, 577–588

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: . . 

Received: 01.10.2008

Citation: Yu. S. Osipov, A. V. Kryazhimskii, V. I. Maksimov, “N. N. Krasovskii's extremal shift method and problems of boundary control”, Avtomat. i Telemekh., 2009, no. 4, 18–30; Autom. Remote Control, 70:4 (2009), 577–588

Citation in format AMSBIB
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\paper N.\,N.~Krasovskii's extremal shift method and problems of boundary control
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\pages 18--30
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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. V. I. Maksimov, “On reconstruction of unknown characteristics of a distributed system using a regularized extremal shift”, Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S188–S203  mathnet  crossref  isi  elib
    2. M. S. Blizorukova, V. I. Maksimov, “An algorithm for dynamic reconstruction of input disturbances from observations of some of the coordinates”, Comput. Math. Math. Phys., 51:6 (2011), 942–951  mathnet  crossref  mathscinet  isi
    3. Maksimov V.I., “The Tracking of the Trajectory of a Dynamical System”, Pmm-J. Appl. Math. Mech., 75:6 (2011), 667–674  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. I. Maksimov, “Ob odnom algoritme dinamicheskogo vosstanovleniya pravoi chasti parabolicheskogo uravneniya”, Sib. zhurn. industr. matem., 16:4 (2013), 94–110  mathnet  mathscinet
    5. M. S. Blizorukova, V. I. Maksimov, “On reconstruction of an input for parabolic equation on infinite time interval”, Russian Math. (Iz. VUZ), 58:8 (2014), 24–34  mathnet  crossref
    6. V. I. Maksimov, “On a problem of linear system control under incomplete information about the phase coordinates”, Autom. Remote Control, 77:6 (2016), 943–958  mathnet  crossref  isi  elib  elib
    7. Maksimov V.I., “Guidance Problem For a Distributed System With Incomplete Information on the State Coordinates and An Unknown Initial State”, Differ. Equ., 52:11 (2016), 1442–1452  crossref  mathscinet  zmath  isi  scopus
    8. V. I. Maksimov, “An algorithm for dynamic reconstruction of the right-hand side of a second-order equation with distributed parameters”, Comput. Math. Math. Phys., 57:8 (2017), 1248–1261  mathnet  crossref  crossref  isi  elib
    9. Maksimov V.I., “Control Problem For a Nonlinear Distributed Equation”, Differ. Equ., 54:11 (2018), 1449–1455  crossref  zmath  isi  scopus
    10. Maksimov V.I., “Guaranteed Control Problem For a Parabolic Equation With Memory”, Differ. Equ., 55:1 (2019), 105–112  crossref  isi  scopus
    11. M. S. Blizorukova, “Dinamicheskii metod nevyazki v zadache rekonstruktsii neizvestnykh kharakteristik sistemy vtorogo poryadka”, Izv. IMI UdGU, 53 (2019), 48–60  mathnet  crossref  elib
    12. V. I. Maksimov, “Ekstremalnyi sdvig v zadache otslezhivaniya resheniya operatornogo differentsialnogo uravneniya”, Tr. IMM UrO RAN, 25, no. 3, 2019, 141–152  mathnet  crossref  elib
    13. Maksimov I V., “Dynamic Reconstruction of Unknown Boundary Disturbances in a Parabolic Equation”, Differ. Equ., 55:11 (2019), 1466–1474  crossref  mathscinet  zmath  isi
    14. V. I. Maksimov, “Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws”, Proc. Steklov Inst. Math., 308 (2020), 208–217  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Maksimov I V., “Modification of the Dynamic Regularization Method For Linear Parabolic Equations”, Differ. Equ., 56:11 (2020), 1452–1462  crossref  mathscinet  zmath  isi
    16. Surkov P.G., “Tracking the Trajectory of a Fractional Dynamical System When Measuring Part of State Vector Coordinates”, Differ. Equ., 56:11 (2020), 1463–1471  crossref  mathscinet  zmath  isi
    17. Kh. Akcha, V. I. Maksimov, “Ustoichivoe granichnoe upravlenie parabolicheskim uravneniem”, Tr. IMM UrO RAN, 27, no. 2, 2021, 7–18  mathnet  crossref  elib
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