IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i18p2224-d632967.html
   My bibliography  Save this article

Adaptive Boundary Control for a Certain Class of Reaction–Advection–Diffusion System

Author

Listed:
  • Oscar F. Murillo-García

    (División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/I.T. La Laguna, Revolución Blvd. and Instituto Tecnológico de La Laguna Av., Torreón 27000, Mexico)

  • Francisco Jurado

    (División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/I.T. La Laguna, Revolución Blvd. and Instituto Tecnológico de La Laguna Av., Torreón 27000, Mexico)

Abstract

Several phenomena in nature are subjected to the interaction of various physical parameters, which, if these latter are well known, allow us to predict the behavior of such phenomena. In most cases, these physical parameters are not exactly known, or even more these are unknown, so identification techniques could be employed in order to estimate their values. Systems for which their inputs and outputs vary both temporally and spatially are the so-called distributed parameter systems (DPSs) modeled through partial differential equations (PDEs). The way in which their parameters evolve with respect to time may not always be known and may also induce undesired behavior of the dynamics of the system. To reverse the above, the well-known adaptive boundary control technique can be used to estimate the unknown parameters assuring a stable behavior of the dynamics of the system. In this work, we focus our attention on the design of an adaptive boundary control for a parabolic type reaction–advection–diffusion PDE under the assumption of unknown parameters for both advection and reaction terms and Robin and Neumann boundary conditions. An identifier PDE system is established and parameter update laws are designed following the certainty equivalence approach with a passive identifier. The performance of the adaptive Neumann stabilizing controller is validated via numerical simulation.

Suggested Citation

  • Oscar F. Murillo-García & Francisco Jurado, 2021. "Adaptive Boundary Control for a Certain Class of Reaction–Advection–Diffusion System," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2224-:d:632967
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/18/2224/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/18/2224/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Pengfei Zheng & Baolin Hou & Mingsong Zou, 2022. "Magnetorheological Fluid of High-Speed Unsteady Flow in a Narrow-Long Gap: An Unsteady Numerical Model and Analysis," Mathematics, MDPI, vol. 10(14), pages 1-25, July.
    2. Francisco Ureña & Ángel García & Antonio M. Vargas, 2022. "Preface to “Applications of Partial Differential Equations in Engineering”," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

    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:18:p:2224-:d:632967. 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.