IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v139y2008i1d10.1007_s10957-008-9430-2.html
   My bibliography  Save this article

Multitime Controllability, Observability and Bang-Bang Principle

Author

Listed:
  • C. Udrişte

    (Polytechnic University of Bucharest)

Abstract

Control problems for multitime first-order PDE arise in many different contexts and ways. The obstruction of complete integrability conditions (path independent curvilinear integrals) has determined the mathematicians to study such problems only in the discrete context, though thus they loose the geometrical character which is proper to the continuous approach. In this paper, we study controllability, observability and bang-bang properties of multitime completely integrable autonomous linear PDE systems, overcoming the existent mathematical prejudices regarding the importance of a multitime evolution of m-flow type. Our geometrical arguments show that each basic theorem has a correspondent in the case of a single-time linear controlled ODE system. The main results include controllability criteria, equivalence between controllability of a PDE system and observability of the dual PDE system, geometry of the control set, extremality and multitime bang-bang principle. All of these show that the passing from controlled single-time evolution (1-flow) to the controlled multitime evolution (m-flow) is not trivial. Changing the geometrical language, the case of nonholonomic evolution can be recovered easily from our theory.

Suggested Citation

  • C. Udrişte, 2008. "Multitime Controllability, Observability and Bang-Bang Principle," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 141-157, October.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:1:d:10.1007_s10957-008-9430-2
    DOI: 10.1007/s10957-008-9430-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9430-2
    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/s10957-008-9430-2?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. S. Pickenhain & M. Wagner, 2005. "Piecewise Continuous Controls in Dieudonné-Rashevsky Type Problems," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 145-163, October.
    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. M. Wagner, 2009. "Pontryagin’s Maximum Principle for Multidimensional Control Problems in Image Processing," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 543-576, March.

    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:139:y:2008:i:1:d:10.1007_s10957-008-9430-2. 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.