IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v136y2008i2d10.1007_s10957-007-9305-y.html
   My bibliography  Save this article

Gradient Descent Approach to Optimal Mode Scheduling in Hybrid Dynamical Systems

Author

Listed:
  • H. Axelsson

    (Kencast)

  • Y. Wardi

    (Georgia Institute of Technology)

  • M. Egerstedt

    (Georgia Institute of Technology)

  • E. I. Verriest

    (Georgia Institute of Technology)

Abstract

This paper concerns the problem of optimally scheduling the sequence of dynamic response functions in nonlinear switched-mode hybrid dynamical systems. The control parameter has a discrete component and a continuous component, namely the sequence of modes and the duration of each mode, while the performance criterion consists of a cost functional on the state trajectory. The problem is naturally cast in the framework of optimal control. This framework has established techniques sufficient to address the continuous part of the parameter, but lacks adequate tools to consider the discrete element. To get around this difficulty, the paper proposes a bilevel hierarchical algorithm. At the lower level, the algorithm considers a fixed mode sequence and minimizes the cost functional with respect to the mode durations; at the upper level, it updates the mode sequence by using a gradient technique that is tailored to the special structure of the discrete variable (mode sequencing). The resulting algorithm is not defined on a single parameter space, but rather on a sequence of Euclidean spaces of increasing dimensions, an unusual setting for which there is no established notion of convergence. The paper suggests first a suitable definition of convergence based on the concepts of optimality functions; then, it proves that the proposed algorithm converges in that sense.

Suggested Citation

  • H. Axelsson & Y. Wardi & M. Egerstedt & E. I. Verriest, 2008. "Gradient Descent Approach to Optimal Mode Scheduling in Hybrid Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 167-186, February.
  • Handle: RePEc:spr:joptap:v:136:y:2008:i:2:d:10.1007_s10957-007-9305-y
    DOI: 10.1007/s10957-007-9305-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9305-y
    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/s10957-007-9305-y?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.

    Citations

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


    Cited by:

    1. Sebastian Sager & Clemens Zeile, 2021. "On mixed-integer optimal control with constrained total variation of the integer control," Computational Optimization and Applications, Springer, vol. 78(2), pages 575-623, March.
    2. Pierre Bonami & Alberto Olivares & Ernesto Staffetti, 2014. "Energy-Optimal Multi-Goal Motion Planning for Planar Robot Manipulators," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 80-104, October.
    3. Xiang Wu & Kanjian Zhang & Changyin Sun, 2013. "Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 454-472, November.

    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:136:y:2008:i:2:d:10.1007_s10957-007-9305-y. 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.