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Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty

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Formal Modeling and Analysis of Timed Systems (FORMATS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11750))

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Abstract

Piecewise Barrier Tubes (PBT) is a new technique for flowpipe overapproximation for nonlinear systems with polynomial dynamics, which leverages a combination of barrier certificates. PBT has advantages over traditional time-step based methods in dealing with those nonlinear dynamical systems in which there is a large difference in speed between trajectories, producing an overapproximation that is time independent. However, the existing approach for PBT is not efficient due to the application of interval methods for enclosure-box computation, and it can only deal with continuous dynamical systems without uncertainty. In this paper, we extend the approach with the ability to handle both continuous and hybrid dynamical systems with uncertainty that can reside in parameters and/or noise. We also improve the efficiency of the method significantly, by avoiding the use of interval-based methods for the enclosure-box computation without loosing soundness. We have developed a C++ prototype implementing the proposed approach and we evaluate it on several benchmarks. The experiments show that our approach is more efficient and precise than other methods in the literature.

This research was supported in part by the Austrian Science Fund (FWF) under grants S11402-N23, S11405-N23 (RiSE/SHiNE), ADynNet (P28182), and Z211-N23 (Wittgenstein Award) and the Deutsche Forschungsgemeinschaft project 389792660-TRR 248.

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Authors and Affiliations

  1. Max-Planck-Institute for Software Systems, Kaiserslautern, Germany

    Hui Kong

  2. IST Austria, Klosterneuburg, Austria

    Thomas A. Henzinger

  3. TU Wien, Vienna, Austria

    Ezio Bartocci

  4. Tsinghua University, Beijing, China

    Yu Jiang

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  1. Hui Kong
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  2. Ezio Bartocci
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  4. Thomas A. Henzinger
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Correspondence to Hui Kong .

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Editors and Affiliations

  1. Université Paris 13, Villetaneuse, France

    Étienne André

  2. University of Twente, Enschede, The Netherlands

    Mariëlle Stoelinga

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Kong, H., Bartocci, E., Jiang, Y., Henzinger, T.A. (2019). Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty. In: André, É., Stoelinga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2019. Lecture Notes in Computer Science(), vol 11750. Springer, Cham. https://doi.org/10.1007/978-3-030-29662-9_8

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