IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v353y2019icp295-307.html
   My bibliography  Save this article

Balanced model reduction of linear systems with nonzero initial conditions: Singular perturbation approximation

Author

Listed:
  • Daraghmeh, Adnan
  • Hartmann, Carsten
  • Qatanani, Naji

Abstract

In this article we study balanced model reduction of linear control systems using the singular perturbation approximation. Balanced model reduction techniques have been successfully applied to systems with homogeneous initial conditions, with one of their most important features being a priori L2 and H∞ bounds for the approximation error. The main focus of this work is to derive an L2 error bound for the singular perturbation approximation for system with inhomogeneous initial conditions, extending related work on balanced truncation. This L2 error bound measures the difference between the input-output maps of the original and of the reduced initial value systems. The advantages and flexibility of this approach are demonstrated with a variety of numerical examples.

Suggested Citation

  • Daraghmeh, Adnan & Hartmann, Carsten & Qatanani, Naji, 2019. "Balanced model reduction of linear systems with nonzero initial conditions: Singular perturbation approximation," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 295-307.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:295-307
    DOI: 10.1016/j.amc.2019.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319300992
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.001?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. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 153-185, September.
    2. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "Erratum to: On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 187-188, September.
    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. Li, Yanpeng & Jiang, Yaolin & Yang, Ping, 2022. "Model order reduction of port-Hamiltonian systems with inhomogeneous initial conditions via approximate finite-time Gramians," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Becker, Simon & Hartmann, Carsten & Redmann, Martin & Richter, Lorenz, 2022. "Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 107-141.

    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. Uzunca, M. & Karasözen, B. & Küçükseyhan, T., 2017. "Moving mesh discontinuous Galerkin methods for PDEs with traveling waves," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 9-18.
    2. Eduardo Casas & Christopher Ryll & Fredi Tröltzsch, 2018. "Optimal control of a class of reaction–diffusion systems," Computational Optimization and Applications, Springer, vol. 70(3), pages 677-707, July.
    3. Peter Nestler & Eckehard Schöll & Fredi Tröltzsch, 2016. "Optimization of nonlocal time-delayed feedback controllers," Computational Optimization and Applications, Springer, vol. 64(1), pages 265-294, May.
    4. Jens Lang & Bernhard A. Schmitt, 2024. "Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 985-1026, October.

    More about this item

    Keywords

    Balanced truncation; Singular perturbation approximation; Error bound; Homogeneous and non-homogeneous initial conditions; L2 norm;
    All these keywords.

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

    Statistics

    Access and download statistics

    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:eee:apmaco:v:353:y:2019:i:c:p:295-307. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.