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Exploiting the Eigenstructure of Linear Systems to Speed up Reachability Computations

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Hybrid Systems Biology (HSB 2014)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 7699))

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Abstract

Reachability analysis has recently proved to be a useful technique for analysing the behaviour of under-specified biological models. In this paper, we propose a method exploiting the eigenstructure of a linear continuous system to efficiently estimate a bounded interval containing the time at which the system can reach a target set from an initial set. Then this estimation can be directly integrated in an existing algorithm for hybrid systems with linear continuous dynamics, to speed up reachability computations. Furthermore, it can also be used to improve time-efficiency of the hybridization technique that is based on a piecewise-linear approximation of non-linear continuous dynamics. The proposed method is illustrated on a number of examples including a biological model.

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Notes

  1. 1.

    H-polytopes are polytopes defined by a set of linear constraints.

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Acknowledgement

We gratefully acknowledge the support of Agence Nationale de la Recherche (ANR) through the CADMIDIA project (grant ANR-13-CESA-0008-03).

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Authors and Affiliations

  1. VERIMAG/CNRS, 2, Avenue de Vignate, 38610, Giere, France

    Alexandre Rocca & Thao Dang

  2. TIMC-IMAG, UMR 5525, UJF-Grenoble 1/CNRS, 38041, Grenoble, France

    Alexandre Rocca & Eric Fanchon

Authors
  1. Alexandre Rocca
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  2. Thao Dang
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  3. Eric Fanchon
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Corresponding author

Correspondence to Alexandre Rocca .

Editor information

Editors and Affiliations

  1. "CNRS-VERIMAG, University of Grenoble-Alpes (UGA), Grenoble, France

    Oded Maler

  2. West Virginia University, Morgantown, West Virginia, USA

    Ádám Halász

  3. VERIMAG, Gieres, France

    Thao Dang

  4. University of Udine, Udine, Italy

    Carla Piazza

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Rocca, A., Dang, T., Fanchon, E. (2015). Exploiting the Eigenstructure of Linear Systems to Speed up Reachability Computations. In: Maler, O., Halász, Á., Dang, T., Piazza, C. (eds) Hybrid Systems Biology. HSB 2014. Lecture Notes in Computer Science(), vol 7699. Springer, Cham. https://doi.org/10.1007/978-3-319-27656-4_7

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  • DOI: https://doi.org/10.1007/978-3-319-27656-4_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27655-7

  • Online ISBN: 978-3-319-27656-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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