IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v153y2012i2d10.1007_s10957-011-9932-1.html
   My bibliography  Save this article

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Author

Listed:
  • N. Haddadi

    (Alzahra University)

  • Y. Ordokhani

    (Alzahra University)

  • M. Razzaghi

    (Mississippi State University)

Abstract

In this paper, a new numerical method for solving the optimal control of linear time-varying delay systems with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions, consisting of block-pulse functions and Bernoulli polynomials, are presented. The operational matrices of integration, product, delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are given. These matrices are then utilized to reduce the solution of the optimal control of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Suggested Citation

  • N. Haddadi & Y. Ordokhani & M. Razzaghi, 2012. "Optimal Control of Delay Systems by Using a Hybrid Functions Approximation," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 338-356, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9932-1
    DOI: 10.1007/s10957-011-9932-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9932-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-011-9932-1?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.

    References listed on IDEAS

    as
    1. F. Khellat, 2009. "Optimal Control of Linear Time-Delayed Systems by Linear Legendre Multiwavelets," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 107-121, 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. Mohamed Karim Bouafoura & Naceur Benhadj Braiek, 2019. "Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    2. Zogheib, Bashar & Tohidi, Emran, 2016. "A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 1-13.
    3. Yusheng Zhou & Zaihua Wang, 2014. "Optimal Feedback Control for Linear Systems with Input Delays Revisited," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 989-1017, December.
    4. Keshavarz, E. & Ordokhani, Y. & Razzaghi, M., 2019. "The Bernoulli wavelets operational matrix of integration and its applications for the solution of linear and nonlinear problems in calculus of variations," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 83-98.
    5. Postavaru, Octavian & Toma, Antonela, 2022. "A numerical approach based on fractional-order hybrid functions of block-pulse and Bernoulli polynomials for numerical solutions of fractional optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 269-284.

    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. Mohamed Karim Bouafoura & Naceur Benhadj Braiek, 2019. "Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems," Complexity, Hindawi, vol. 2019, pages 1-14, April.

    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:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9932-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.