IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v183y2019i1d10.1007_s10957-019-01537-4.html
   My bibliography  Save this article

A Variation Evolving Method for Optimal Control Computation

Author

Listed:
  • Sheng Zhang

    (China Aerodynamics Research and Development Center)

  • En-Mi Yong

    (China Aerodynamics Research and Development Center)

  • Wei-Qi Qian

    (China Aerodynamics Research and Development Center)

  • Kai-Feng He

    (China Aerodynamics Research and Development Center)

Abstract

A new method, which originates from the continuous-time dynamics stability theory in the control field, is proposed for the optimal control computation. By introducing a virtual dimension, the variation time, an infinite-dimensional dynamic system that describes the variation motion of variables is derived from the optimal control problem based on the Lyapunov principle. The optimal solution is its stable equilibrium point and will be obtained in an asymptotically evolving way. Through this method, the intractable optimal control problems are transformed to the initial-value problems and they may be solved with mature ordinary differential equation numerical integration methods. Especially, the deduced dynamic system is globally stable, so any initial value may evolve to an extremal solution ultimately.

Suggested Citation

  • Sheng Zhang & En-Mi Yong & Wei-Qi Qian & Kai-Feng He, 2019. "A Variation Evolving Method for Optimal Control Computation," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 246-270, October.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:1:d:10.1007_s10957-019-01537-4
    DOI: 10.1007/s10957-019-01537-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01537-4
    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/s10957-019-01537-4?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. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
    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. Mauro Pontani, 2021. "Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 545-574, December.
    2. Mauro Pontani & Bruce Conway, 2014. "Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 272-292, July.
    3. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    4. Calvin Kielas-Jensen & Venanzio Cichella & David Casbeer & Satyanarayana Gupta Manyam & Isaac Weintraub, 2021. "Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 899-916, December.
    5. David Ottesen & Ryan P. Russell, 2021. "Unconstrained Direct Optimization of Spacecraft Trajectories Using Many Embedded Lambert Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 634-674, December.
    6. N. Koeppen & I. M. Ross & L. C. Wilcox & R. J. Proulx, 2019. "Fast Mesh Refinement in Pseudospectral Optimal Control," Papers 1904.12992, arXiv.org.
    7. Alena Vagaská & Miroslav Gombár & Ľuboslav Straka, 2022. "Selected Mathematical Optimization Methods for Solving Problems of Engineering Practice," Energies, MDPI, vol. 15(6), pages 1-22, March.
    8. Miguel G. Villarreal-Cervantes, 2017. "Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 628-657, May.

    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:183:y:2019:i:1:d:10.1007_s10957-019-01537-4. 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.