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Stable Adaptive Co-simulation: A Switched Systems Approach

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IUTAM Symposium on Solver-Coupling and Co-Simulation

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 35))

Abstract

Co-simulation promotes the idea that domain specific simulation tools should cooperate in order to simulate the inter-domain interactions that are often observed in complex systems. To get trustworthy results, it is important that this technique preserves the stability properties of the original system. In this paper, we show how to preserve stability for adaptive co-simulation schemes, which offer fine grained control over the performance/accuracy of the co-simulation. To this end, we apply the joint spectral radius theory to certify that an adaptive co-simulation scheme is stable, and, if that is not possible, we use recent results in this field to create a trace of decisions that lead to instability. With this trace, it is possible to adjust the adaptive co-simulation in order to make it stable. Our approach is limited by the fact that computing the joint spectral radius is NP-Hard and undecidable in general. Nevertheless, we successfully applied our results to the co-simulation of a double mass-spring-damper system.

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Notes

  1. 1.

    Two well known standards for co-simulation—the Functional Mockup Interface Standard for co-simulation [10], and the High Level Architecture [1]—share this assumption.

  2. 2.

    http://msdl.cs.mcgill.ca/people/claudio/hybrid_cosim_analysis.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Cláudio Gomes & Hans Vangheluwe

  2. Université catholique de Louvain, ICTEAM, Ottignies-Louvain-la-Neuve, Belgium

    Benoît Legat & Raphaël M. Jungers

  3. Flanders Make, Lommel, Belgium

    Cláudio Gomes & Hans Vangheluwe

  4. School of Computer Science, McGill University, Montreal, QC, Canada

    Hans Vangheluwe

Authors
  1. Cláudio Gomes
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  2. Benoît Legat
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  3. Raphaël M. Jungers
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  4. Hans Vangheluwe
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Correspondence to Cláudio Gomes .

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  1. Institut für Angewandte Dynamik, Technische Universität Darmstadt, Darmstadt, Germany

    Bernhard Schweizer

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Gomes, C., Legat, B., Jungers, R.M., Vangheluwe, H. (2019). Stable Adaptive Co-simulation: A Switched Systems Approach. In: Schweizer, B. (eds) IUTAM Symposium on Solver-Coupling and Co-Simulation. IUTAM Bookseries, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-030-14883-6_5

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