IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3218-d701130.html
   My bibliography  Save this article

Guaranteed Estimation of Solutions to the Cauchy Problem When the Restrictions on Unknown Initial Data Are Not Posed

Author

Listed:
  • Oleksandr Nakonechnyi

    (Faculty of Computer Science and Cybernetics, National Taras Shevchenko University of Kiev, 03680 Kiev, Ukraine
    Faculty of Engineering and Sustainable Development, Academy of Technology and Environment, University of Gävle, 80176 Gävle, Sweden
    These authors contributed equally to this work.)

  • Yuri Podlipenko

    (Faculty of Computer Science and Cybernetics, National Taras Shevchenko University of Kiev, 03680 Kiev, Ukraine
    These authors contributed equally to this work.)

  • Yury Shestopalov

    (Faculty of Engineering and Sustainable Development, Academy of Technology and Environment, University of Gävle, 80176 Gävle, Sweden)

Abstract

The paper deals with Cauchy problems for first-order systems of linear ordinary differential equations with unknown data. It is assumed that the right-hand sides of equations belong to certain bounded sets in the space of square-integrable vector-functions, and the information about the initial conditions is absent. From indirect noisy observations of solutions to the Cauchy problems on a finite system of points and intervals, the guaranteed mean square estimates of linear functionals on unknown solutions of the problems under consideration are obtained. Under an assumption that the statistical characteristics of noise in observations are not known exactly, it is proved that such estimates can be expressed in terms of solutions to well-defined boundary value problems for linear systems of impulsive ordinary differential equations.

Suggested Citation

  • Oleksandr Nakonechnyi & Yuri Podlipenko & Yury Shestopalov, 2021. "Guaranteed Estimation of Solutions to the Cauchy Problem When the Restrictions on Unknown Initial Data Are Not Posed," Mathematics, MDPI, vol. 9(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3218-:d:701130
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3218/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3218/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3218-:d:701130. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.