IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v153y2012i2d10.1007_s10957-011-9976-2.html
   My bibliography  Save this article

Non-recursive Haar Connection Coefficients Based Approach for Linear Optimal Control

Author

Listed:
  • Monika Garg

    (National Institute of Technology)

  • Lillie Dewan

    (National Institute of Technology)

Abstract

In the present paper, two-fold contributions are made. First, non-recursive formulations of various Haar operational matrices, such as Haar connection coefficients matrix, backward integral matrix, and product matrix are developed. These non-recursive formulations result in computationally efficient algorithms, with respect to execution time and stack-and-memory overflows in computer implementations, as compared to corresponding recursive formulations. This is demonstrated with the help of MATLAB PROFILER. Later, a unified method is proposed, based on these non-recursive connection coefficients, for solving linear optimal control problems of all types, irrespective of order and nature of the system. This means that the single method is capable of optimizing both time-invariant and time-varying linear systems of any order efficiently; it has not been reported in the literature so far. The proposed method is applied to solve finite horizon LQR problems with final state control. Computational efficiency of the proposed method is established with the help of comparison on computation-time at different resolutions by taking several illustrative examples.

Suggested Citation

  • Monika Garg & Lillie Dewan, 2012. "Non-recursive Haar Connection Coefficients Based Approach for Linear Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 320-337, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9976-2
    DOI: 10.1007/s10957-011-9976-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9976-2
    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/s10957-011-9976-2?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. C. H. Hsiao & W. J. Wang, 1999. "Optimal Control of Linear Time-Varying Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 641-655, December.
    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. Hsiao, C.H., 2004. "Haar wavelet approach to linear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 561-567.
    2. Hsiao, Chun-Hui & Wang, Wen-June, 2001. "Haar wavelet approach to nonlinear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 347-353.
    3. R. Dai & J. E. Cochran, 2009. "Wavelet Collocation Method for Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 265-278, November.
    4. T. Binder & L. Blank & W. Dahmen & W. Marquardt, 2001. "Iterative Algorithms for Multiscale State Estimation, Part 1: Concepts," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 501-527, December.
    5. C. H. Hsiao & W. J. Wang, 1999. "State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 623-640, December.
    6. Tian, Yongge & Herzberg, Agnes M., 2006. "A-minimax and D-minimax robust optimal designs for approximately linear Haar-wavelet models," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2942-2951, June.
    7. Hsiao, Chun-Hui, 2004. "Haar wavelet direct method for solving variational problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 569-585.

    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_s10957-011-9976-2. 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.