IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/7908378.html
   My bibliography  Save this article

A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems

Author

Listed:
  • Binfeng Pan
  • Yang Wang
  • Shaohua Tian

Abstract

Solving hypersensitive optimal control problems is a long-standing challenge for decades in optimization engineering, mainly due to the possible nonexistence of the optimal solution to meet the required error tolerance under double-precision arithmetic and the hypersensitivity of the optimal solution with respect to the initial conditions. In this paper, a new high-precision single shooting method is presented to address the above two difficulties. Multiple-precision arithmetic and Taylor series method are introduced to provide the accurate optimal solution with arbitrary higher significant digits and arbitrary higher integral accuracy, respectively. Besides, a new modified bidirectional single shooting method is developed, which fully utilizes the three-segment structure of the hypersensitive optimal control problems and provides appropriate initial guess that is close to the optimal solutions. Numerical demonstrations in a typical hypersensitive optimal control problem are presented to illustrate the effectiveness of this new method, which indicates that the accurate optimal solution of this challenging problem can be easily solved by this simple single shooting method within several iterations.

Suggested Citation

  • Binfeng Pan & Yang Wang & Shaohua Tian, 2018. "A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-11, April.
  • Handle: RePEc:hin:jnlmpe:7908378
    DOI: 10.1155/2018/7908378
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2018/7908378.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/MPE/2018/7908378.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2018/7908378?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
    ---><---

    Citations

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


    Cited by:

    1. Kristofer Drozd & Roberto Furfaro & Andrea D’Ambrosio, 2024. "A Theory of Functional Connections-Based hp -Adaptive Mesh Refinement Algorithm for Solving Hypersensitive Two-Point Boundary-Value Problems," Mathematics, MDPI, vol. 12(9), pages 1-35, April.

    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:hin:jnlmpe:7908378. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.