IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1836-d825094.html
   My bibliography  Save this article

Identification of Quadratic Volterra Polynomials in the “Input–Output” Models of Nonlinear Systems

Author

Listed:
  • Yury Voscoboynikov

    (Department of Applied Mathematics, Novosibirsk State University of Architecture and Civil Engineering, 630008 Novosibirsk, Russia
    Department of Automation, Novosibirsk State Technical University, 630087 Novosibirsk, Russia)

  • Svetlana Solodusha

    (Department of Applied Mathematics, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia)

  • Evgeniia Markova

    (Department of Applied Mathematics, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia)

  • Ekaterina Antipina

    (Department of Applied Mathematics, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
    Department of Mathematical Analysis and Differential Equations, Irkutsk State University, 664003 Irkutsk, Russia)

  • Vasilisa Boeva

    (Department of Applied Mathematics, Novosibirsk State University of Architecture and Civil Engineering, 630008 Novosibirsk, Russia)

Abstract

In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integro-power series (polynomial). We consider nonparametric identification of models using physically realizable piecewise linear test signals in the time domain. The advantage of the presented approach is to obtain explicit formulas for calculating the transient responses (Volterra kernels), which determine the unique solution of the Volterra integral equations of the first kind with two variable integration limits. The numerical method proposed in the paper for solving the corresponding equations includes the use of smoothing splines. An important result is that the constructed identification algorithm has a low methodological error.

Suggested Citation

  • Yury Voscoboynikov & Svetlana Solodusha & Evgeniia Markova & Ekaterina Antipina & Vasilisa Boeva, 2022. "Identification of Quadratic Volterra Polynomials in the “Input–Output” Models of Nonlinear Systems," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1836-:d:825094
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1836/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1836/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gábor Balassa, 2022. "Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model," Mathematics, MDPI, vol. 10(8), pages 1-21, April.
    2. A. S. Apartsyn & S. V. Solodusha & V. A. Spiryaev, 2013. "Modeling of Nonlinear Dynamic Systems with Volterra Polynomials: Elements of Theory and Applications," International Journal of Energy Optimization and Engineering (IJEOE), IGI Global, vol. 2(4), pages 16-43, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Natalia Bakhtadze, 2023. "Preface to the Special Issue on “Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control”—Special Issue Book," Mathematics, MDPI, vol. 11(8), pages 1-3, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Svetlana Solodusha & Mikhail Bulatov, 2021. "Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering," Mathematics, MDPI, vol. 9(16), pages 1-18, August.

    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:10:y:2022:i:11:p:1836-:d:825094. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.