IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v51y2020i5p786-810.html
   My bibliography  Save this article

Derivative-orthogonal wavelets for discretizing constrained optimal control problems

Author

Listed:
  • E. Ashpazzadeh
  • B. Han
  • M. Lakestani
  • M. Razzaghi

Abstract

In this article, a pair of wavelets for Hermite cubic spline bases are presented. These wavelets are in $C^{1} $C1 and supported on $[-1,1] $[−1,1]. These spline wavelets are then adapted to the interval $[0,1] $[0,1] and we prove that they form a Riesz wavelet in $L_2([0,1]) $L2([0,1]). The wavelet bases are used to solve the linear optimal control problems. The operational matrices of integration and product are then utilised to reduce the given optimisation problems to the system of algebraic equations. Because of the sparsity nature of these matrices, this method is computationally very attractive and reduces CPU time and computer memory. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Suggested Citation

  • E. Ashpazzadeh & B. Han & M. Lakestani & M. Razzaghi, 2020. "Derivative-orthogonal wavelets for discretizing constrained optimal control problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(5), pages 786-810, April.
    • Handle: RePEc:taf:tsysxx:v:51:y:2020:i:5:p:786-810
    DOI: 10.1080/00207721.2020.1739356
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2020.1739356
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2020.1739356?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Mohammad, Mutaz & Trounev, Alexander, 2020. "Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications to hematopoietic stem cell modeling," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

    More about this item

    Statistics

    Access and download statistics

    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:taf:tsysxx:v:51:y:2020:i:5:p:786-810. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TSYS20 .

    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.