IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v86y2023i2d10.1007_s10898-022-01261-w.html
   My bibliography  Save this article

A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems

Author

Listed:
  • Andreas Ernst

    (Monash University)

  • Lars Grüne

    (University of Bayreuth)

  • Janosch Rieger

    (Monash University)

Abstract

The infinite time reachable set of a strictly stable linear control system is the Hausdorff limit of the finite time reachable set of the origin as time tends to infinity. By definition, it encodes useful information on the long-term behavior of the control system. Its characterization as a limit set gives rise to numerical methods for its computation that are based on forward iteration of approximate finite time reachable sets. These methods tend to be computationally expensive, because they essentially perform a Minkowski sum in every single forward step. We develop a new approach to computing the infinite time reachable set that is based on the invariance properties of the control system and the desired set. These allow us to characterize a polyhedral outer approximation as the unique solution to a linear program with constraints that incorporate the system dynamics. In particular, this approach does not rely on forward iteration of finite time reachable sets.

Suggested Citation

  • Andreas Ernst & Lars Grüne & Janosch Rieger, 2023. "A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems," Journal of Global Optimization, Springer, vol. 86(2), pages 521-543, June.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:2:d:10.1007_s10898-022-01261-w
    DOI: 10.1007/s10898-022-01261-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01261-w
    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/s10898-022-01261-w?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. C. E. T. Dórea & J. C. Hennet, 1999. "(A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 521-542, December.
    2. Ilya Kolmanovsky & Elmer G. Gilbert, 1998. "Theory and computation of disturbance invariant sets for discrete-time linear systems," Mathematical Problems in Engineering, Hindawi, vol. 4, pages 1-51, January.
    3. Janosch Rieger, 2021. "A Galerkin approach to optimization in the space of convex and compact subsets of $${\mathbb {R}}^d$$ R d," Journal of Global Optimization, Springer, vol. 79(3), pages 593-615, March.
    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. Jiao, Feixiang & Zou, Yuan & Zhang, Xudong & Zhang, Bin, 2022. "Online optimal dispatch based on combined robust and stochastic model predictive control for a microgrid including EV charging station," Energy, Elsevier, vol. 247(C).

    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:jglopt:v:86:y:2023:i:2:d:10.1007_s10898-022-01261-w. 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.