IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2125-d841996.html
   My bibliography  Save this article

Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems

Author

Listed:
  • Bruno Dogančić

    (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

  • Marko Jokić

    (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

  • Neven Alujević

    (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

  • Hinko Wolf

    (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia)

Abstract

The paper deals with uncertainty modelling, robust stability and performance analysis of multi-input multi-output (MIMO) reduced order spatially distributed dissipative dynamical systems. While researching the topic of modern robust control of such systems, two key findings were discovered: (i) systematic modelling of the uncertainty and model order reduction (MOR) at the level of a subsystem gives both modelling freedom and the ability for obtaining less conservative uncertainties on the level of a subsystem; (ii) for a special class of interconnected dissipative dynamical systems, uncertainty conservatism at the subsystem level can be reduced—a novel, structure preserving algorithm employing subsystem partitioning and subsystem MOR by means of balanced truncation method (BTM) is used to obtain low-order robustly stable interconnected systems. Such systems are suitable for practical decentralized and distributed robust controller synthesis. Built upon a powerful framework of integral quadratic constraints (IQCs), this approach gives uncertainty modelling flexibility to perform robustness analysis of real world interconnected systems that are usually affected by multiple types of uncertainties at once. The proposed uncertainty modelling procedure and its practical application are presented on the numerical example. A spatially discretized vibration dynamical system comprised of a series of simply supported Euler beams mutually interconnected by springs and dampers is examined. Spatial discretization of the mathematical model is carried out using the finite element method (FEM).

Suggested Citation

  • Bruno Dogančić & Marko Jokić & Neven Alujević & Hinko Wolf, 2022. "Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems," Mathematics, MDPI, vol. 10(12), pages 1-31, June.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2125-:d:841996
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2125/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/12/2125/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xinsheng Wang & Shimin Fan & Ming-Zhe Dai & Chengxi Zhang, 2021. "On Model Order Reduction of Interconnect Circuit Network: A Fast and Accurate Method," Mathematics, MDPI, vol. 9(11), pages 1-13, May.
    2. Timo Reis & Tatjana Stykel, 2007. "Stability analysis and model order reduction of coupled systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 13(5), pages 413-436, October.
    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. Alexey V. Yakovlev & Vladimir V. Alekseev & Maria V. Volchikhina & Sergey V. Petrenko, 2022. "A Combinatorial Model for Determining Information Loss in Organizational and Technical Systems," Mathematics, MDPI, vol. 10(19), pages 1-12, September.

    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. Karasözen, Bülent & Mülayim, Gülden & Uzunca, Murat & Yıldız, Süleyman, 2021. "Reduced order modelling of nonlinear cross-diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    2. Uzunca, Murat & Karasözen, Bülent & Yıldız, Süleyman, 2021. "Structure-preserving reduced-order modeling of Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 193-211.
    3. Karasözen, Bülent & Yıldız, Süleyman & Uzunca, Murat, 2022. "Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation," Applied Mathematics and Computation, Elsevier, vol. 421(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:gam:jmathe:v:10:y:2022:i:12:p:2125-:d:841996. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.