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Clustering-Based Model Order Reduction for Nonlinear Network Systems

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Model Reduction of Complex Dynamical Systems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 171))

Abstract

Clustering by projection has been proposed as a way to preserve network structure in linear multi-agent systems. Here, we extend this approach to a class of nonlinear network systems. Additionally, we generalize our clustering method which restores the network structure in an arbitrary reduced-order model obtained by projection. We demonstrate this method on a number of examples.

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Acknowledgements

This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under the project SA 3477/1-1.

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Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

    Peter Benner, Sara Grundel & Petar Mlinarić

Authors
  1. Peter Benner
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  2. Sara Grundel
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  3. Petar Mlinarić
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Corresponding author

Correspondence to Petar Mlinarić .

Editor information

Editors and Affiliations

  1. Dynamics of Complex Technical Systems, Max Planck Institute, Magdeburg, Sachsen-Anhalt, Germany

    Peter Benner

  2. Institute of Mathematics, Technical University of Berlin, Berlin, Germany

    Tobias Breiten

  3. Institute for Numerical Analysis, TU Braunschweig, Braunschweig, Germany

    Heike Faßbender

  4. Mathematisches Institut, Universität Koblenz-Landau, Campus Koblenz, Koblenz, Germany

    Michael Hinze

  5. Institut für Mathematik, Universität Augsburg, Augsburg, Germany

    Tatjana Stykel

  6. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Ralf Zimmermann

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Benner, P., Grundel, S., Mlinarić, P. (2021). Clustering-Based Model Order Reduction for Nonlinear Network Systems. In: Benner, P., Breiten, T., Faßbender, H., Hinze, M., Stykel, T., Zimmermann, R. (eds) Model Reduction of Complex Dynamical Systems. International Series of Numerical Mathematics, vol 171. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-72983-7_4

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