IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4615-0095-7_3.html

Optimal impulse control problem with restricted number of impulses

In: Impulsive Control in Continuous and Discrete-Continuous Systems

Author

Listed:
  • Boris M. Miller

    (Institute for Information Transmission Problems)

  • Evgeny Ya. Rubinovich

    (Institute of Control Sciences)

Abstract

The classical statement of the impulse control problems [73], [98], [122], [218], [121] presumes, as a rule, the energy type constraints to be imposed on the total intensity of control actions. However, if there are no restrictions that are imposed on the total number of impulses or/and on the impulse repetition rate, then the impulse sliding mode can appear as an optimal solutions (see [73], [122] and Examples 1.2 and 1.3). The realization of such modes needs the extremely high impulse repetition rate, which may be illegal in some technical systems. One of the available method with these constraints to be taken into account is to restate the optimal control problem as a problem of mathematical programming. In this way one can obtain the optimality conditions of a Khun-Tucker’s type and solve the problem somehow with the aid of numerical procedures. Meanwhile in the optimal control problems there are some more powerful tools, like the Pontriagin maximum principle [18], [59], [169] which is much more effective, than mathematical programming methods. However, to derive the maximum principle in DCS, one has to justify the convexity of the attainability set for the system state after one impulse application [3], [4], [206]. Generally it is rather a complicated problem which can be effectively solved only for linear systems.

Suggested Citation

  • Boris M. Miller & Evgeny Ya. Rubinovich, 2003. "Optimal impulse control problem with restricted number of impulses," Springer Books, in: Impulsive Control in Continuous and Discrete-Continuous Systems, chapter 0, pages 103-136, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-0095-7_3
    DOI: 10.1007/978-1-4615-0095-7_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprchp:978-1-4615-0095-7_3. 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: 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.