IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p706-d1347784.html
   My bibliography  Save this article

A Stabilisation System Synthesis for Motion along a Preset Trajectory and Its Solution by Symbolic Regression

Author

Listed:
  • Askhat Diveev

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova Str., 44, Build. 2, 119333 Moscow, Russia)

  • Elena Sofronova

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova Str., 44, Build. 2, 119333 Moscow, Russia)

  • Nurbek Konyrbaev

    (Institute of Engineering and Technology, Korkyt Ata Kyzylorda University, Aiteke bi Str. 29A, Kyzylorda 120014, Kazakhstan)

Abstract

The problem of a stabilisation system synthesis for the motion of a control object along a given spatial trajectory is considered. The complexity of the problem is that the preset trajectory is defined in the state subspace and not in time. This paper describes a stabilisation system synthesis for motion along a trajectory specified in time and along a trajectory specified in the form of a manifold in a state space. In order to construct a stabilisation system, it is necessary to determine a distance between an object and the given trajectory at each moment in time. For trajectories that are not given in time, the determination of this distance can be ambiguous. An object may be exactly on a trajectory but at a different time. This paper proposes some approaches to solve the problem. One of the approaches is to transform a given trajectory in a state subspace into a trajectory given in time. A description of a universal method to perform this transformation is presented. In order to solve the synthesis problem automatically, without having to analyse the mathematical model of the control object, it is suggested that machine learning control by symbolic regression is used. In computational experiments, examples of stabilisation system syntheses for quadcopter motion along a given spatial trajectory are presented.

Suggested Citation

  • Askhat Diveev & Elena Sofronova & Nurbek Konyrbaev, 2024. "A Stabilisation System Synthesis for Motion along a Preset Trajectory and Its Solution by Symbolic Regression," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:706-:d:1347784
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/706/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/706/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Askhat Diveev & Elena Sofronova, 2023. "Universal Stabilisation System for Control Object Motion along the Optimal Trajectory," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    Full references (including those not matched with items on IDEAS)

    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. Askhat Diveev & Elena Sofronova & Nurbek Konyrbaev & Oralbek Abdullayev, 2024. "Advanced Model with a Trajectory Tracking Stabilisation System and Feasible Solution of the Optimal Control Problem," Mathematics, MDPI, vol. 12(20), pages 1-20, October.

    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:12:y:2024:i:5:p:706-:d:1347784. 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.