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A Statistical Approach for Computing Reachability of Non-linear and Stochastic Dynamical Systems

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Book cover Quantitative Evaluation of Systems (QEST 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8657))

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Abstract

We present a novel approach to compute reachable sets of dynamical systems with uncertain initial conditions or parameters, leveraging state-of-the-art statistical techniques. From a small set of samples of the true reachable function of the system, expressed as a function of initial conditions or parameters, we emulate such function using a Bayesian method based on Gaussian Processes. Uncertainty in the reconstruction is reflected in confidence bounds which, when combined with template polyhedra ad optimised, allow us to bound the reachable set with a given statistical confidence. We show how this method works straightforwardly also to do reachability computations for uncertain stochastic models.

G.S. acknowledges support from the ERC under grant MLCS 306999. L.B. acknowledges partial support from EU-FET project QUANTICOL (nr. 600708) and by FRA-UniTS.

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Author information

Authors and Affiliations

  1. DMG, University of Trieste, and CNR/ISTI, Pisa, Italy

    Luca Bortolussi

  2. School of Informatics, University of Edinburgh, UK

    Guido Sanguinetti

  3. SynthSys, Centre for Synthetic and Systems Biology, University of Edinburgh, UK

    Guido Sanguinetti

Authors
  1. Luca Bortolussi
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  2. Guido Sanguinetti
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Editor information

Editors and Affiliations

  1. School of Computing Science, University of Glasgow, G12 8RZ, Glasgow, UK

    Gethin Norman

  2. University of Illinois, 61801-2918, Urbana, IL, USA

    William Sanders

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Bortolussi, L., Sanguinetti, G. (2014). A Statistical Approach for Computing Reachability of Non-linear and Stochastic Dynamical Systems. In: Norman, G., Sanders, W. (eds) Quantitative Evaluation of Systems. QEST 2014. Lecture Notes in Computer Science, vol 8657. Springer, Cham. https://doi.org/10.1007/978-3-319-10696-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-10696-0_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10695-3

  • Online ISBN: 978-3-319-10696-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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