IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v123y2004i3d10.1007_s10957-004-5725-0.html
   My bibliography  Save this article

Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems

Author

Listed:
  • K. Malanowski

    (Polish Academy of Sciences)

  • H. Maurer

    (Westfälische Wilhelms-Universität)

  • S. Pickenhain

    (Westfälische Wilhelms-Universität)

Abstract

Second-order sufficient optimality conditions (SSC) are derived for an optimal control problem subject to mixed control-state and pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits the regularity of the control function as well as the associated Lagrange multipliers. The obtained SSC involve the strict Legendre-Clebsch condition and the solvability of an auxiliary Riccati equation. They are weakened by taking into account the strongly active constraints.

Suggested Citation

  • K. Malanowski & H. Maurer & S. Pickenhain, 2004. "Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 595-617, December.
  • Handle: RePEc:spr:joptap:v:123:y:2004:i:3:d:10.1007_s10957-004-5725-0
    DOI: 10.1007/s10957-004-5725-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-004-5725-0
    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/s10957-004-5725-0?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. Dirk Augustin & Helmut Maurer, 2001. "Computational Sensitivity Analysis for State Constrained Optimal Control Problems," Annals of Operations Research, Springer, vol. 101(1), pages 75-99, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. M. Gerdts, 2006. "Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 443-462, September.
    2. M. M. A. Ferreira & A. F. Ribeiro & G. V. Smirnov, 2015. "Local Minima of Quadratic Functionals and Control of Hydro-electric Power Stations," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 985-1005, June.
    3. Leonardo Mazzini, 2023. "Neighboring Optimal Guidance in Bang Bang Control with Target," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 310-336, October.
    4. Gerardo Sánchez Licea, 2021. "Weak Measurable Optimal Controls for the Problems of Bolza," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    5. Enes Kacapor & Teodor M. Atanackovic & Cemal Dolicanin, 2020. "Optimal Shape and First Integrals for Inverted Compressed Column," Mathematics, MDPI, vol. 8(3), pages 1-14, March.

    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.

      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:123:y:2004:i:3:d:10.1007_s10957-004-5725-0. 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.