IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v184y2020i2d10.1007_s10957-019-01597-6.html
   My bibliography  Save this article

Abnormal and Singular Solutions in the Target Guarding Problem with Dynamics

Author

Listed:
  • Matthew W. Harris

    (Utah State University)

Abstract

The topic of this paper is a two-player zero-sum differential game known as the target guarding problem. After a brief review of Isaacs’ original problem and solution, a problem with second-order dynamics and acceleration control is considered. It is shown that there are four solution classes satisfying the necessary conditions. The four classes are (i) abnormal and non-singular, (ii) normal and non-singular, (iii) normal and pursuer singular, (iv) normal and evader singular. The normal and totally singular case is ruled out. Closed-form solutions are provided for cases ii–iv. The order of singularity in all cases is infinite. Thus, the problem exhibits many interesting properties: normality, abnormality, non-singularity, infinite-order singularity, and non-uniqueness. A practical example of each class is provided.

Suggested Citation

  • Matthew W. Harris, 2020. "Abnormal and Singular Solutions in the Target Guarding Problem with Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 627-643, February.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01597-6
    DOI: 10.1007/s10957-019-01597-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01597-6
    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/s10957-019-01597-6?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. Matthew W. Harris & Behçet Açıkmeşe, 2014. "Maximum Divert for Planetary Landing Using Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 975-995, September.
    2. H. Ehtamo & T. Raivio, 2001. "On Applied Nonlinear and Bilevel Programming or Pursuit-Evasion Games," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 65-96, January.
    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. Yu Wang & Xiangtong Qi, 2017. "Evasion policies for a vessel being chased by pirate skiffs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(6), pages 453-475, September.

    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:184:y:2020:i:2:d:10.1007_s10957-019-01597-6. 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.