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International Conference on Formal Modeling and Analysis of Timed Systems

FORMATS 2020: Formal Modeling and Analysis of Timed Systems pp 265–282Cite as

Reachability Analysis of Nonlinear Systems Using Hybridization and Dynamics Scaling

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12288))

Abstract

Reachability analysis techniques aim to compute which states a dynamical system can enter. The analysis of systems described by nonlinear differential equations is known to be particularly challenging. Hybridization methods tackle this problem by abstracting nonlinear dynamics with piecewise linear dynamics around the reachable states, with additional inputs to ensure overapproximation. This reduces the analysis of a system with nonlinear dynamics to the one with piecewise affine dynamics, which have powerful analysis methods. In this paper, we present improvements to the hybridization approach based on a dynamics scaling model transformation. The transformation aims to reduce the sizes of the linearization domains, and therefore reduces overapproximation error. We showcase the efficiency of our approach on a number of nonlinear benchmark instances, and compare our approach with Flow*.

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Notes

  1. 1.

    https://ths.rwth-aachen.de/research/projects/hypro/biological-model-i/.

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Acknowledgments

This research was supported in part by the Air Force Office of Scientific Research under award numbers FA2386-17-1-4065 and FA9550-19-1-0288. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force.

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Authors and Affiliations

  1. Australian National University, Canberra, Australia

    Dongxu Li & Sergiy Bogomolov

  2. Newcastle University, Newcastle upon Tyne, UK

    Sergiy Bogomolov

  3. Stony Brook University, Stony Brook, NY, USA

    Stanley Bak

Authors
  1. Dongxu Li
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  2. Stanley Bak
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  3. Sergiy Bogomolov
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Correspondence to Sergiy Bogomolov .

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Editors and Affiliations

  1. Inria, Université de Rennes, Rennes, France

    Nathalie Bertrand

  2. Radboud University, Nijmegen, The Netherlands

    Nils Jansen

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Li, D., Bak, S., Bogomolov, S. (2020). Reachability Analysis of Nonlinear Systems Using Hybridization and Dynamics Scaling. In: Bertrand, N., Jansen, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2020. Lecture Notes in Computer Science(), vol 12288. Springer, Cham. https://doi.org/10.1007/978-3-030-57628-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-57628-8_16

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