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Structure-Preserving Model Reduction of Physical Network Systems

In: Realization and Model Reduction of Dynamical Systems

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  • Arjan van der Schaft

    (University of Groningen, Bernoulli Institute and Jan C. Willems Center for Systems and Control)

Abstract

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).

Suggested Citation

  • Arjan van der Schaft, 2022. "Structure-Preserving Model Reduction of Physical Network Systems," Springer Books, in: Christopher Beattie & Peter Benner & Mark Embree & Serkan Gugercin & Sanda Lefteriu (ed.), Realization and Model Reduction of Dynamical Systems, pages 299-314, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95157-3_16
    DOI: 10.1007/978-3-030-95157-3_16
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