IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v130y2006i3d10.1007_s10957-006-9121-9.html
   My bibliography  Save this article

Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two

Author

Listed:
  • M. Gerdts

    (University of Hamburg)

Abstract

Necessary conditions in terms of a local minimum principle are derived for optimal control problems subject to index-2 differential-algebraic equations, pure state constraints, and mixed control-state constraints. Differential-algebraic equations are composite systems of differential equations and algebraic equations, which arise frequently in practical applications. The local minimum principle is based on the necessary optimality conditions for general infinite optimization problems. The special structure of the optimal control problem under consideration is exploited and allows us to obtain more regular representations for the multipliers involved. An additional Mangasarian-Fromowitz-like constraint qualification for the optimal control problem ensures the regularity of a local minimum. An illustrative example completes the article.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:3:d:10.1007_s10957-006-9121-9
    DOI: 10.1007/s10957-006-9121-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9121-9
    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/s10957-006-9121-9?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. 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.
    2. M. Gerdts, 2003. "Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 267-294, May.
    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. "Representation of the Lagrange Multipliers for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 231-251, August.
    2. Matthias Gerdts & Martin Kunkel, 2011. "A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 601-633, April.
    3. Matthias Gerdts & Björn Hüpping, 2012. "Virtual control regularization of state constrained linear quadratic optimal control problems," Computational Optimization and Applications, Springer, vol. 51(2), pages 867-882, 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.
    1. 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.
    2. E. Trélat, 2012. "Optimal Control and Applications to Aerospace: Some Results and Challenges," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 713-758, September.
    3. Gerdts, Matthias, 2008. "A nonsmooth Newton’s method for control-state constrained optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 925-936.
    4. 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.
    5. Jinhai Chen & Herschel Rabitz, 2019. "On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 518-535, February.
    6. Matthias Gerdts & Martin Kunkel, 2011. "A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 601-633, April.
    7. Gerardo Sánchez Licea, 2021. "Weak Measurable Optimal Controls for the Problems of Bolza," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    8. M. Gerdts, 2006. "Representation of the Lagrange Multipliers for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 231-251, August.
    9. 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.

    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:130:y:2006:i:3:d:10.1007_s10957-006-9121-9. 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.