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Hybrid Tools for Hybrid Systems – Proving Stability and Safety at Once

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Book cover Formal Modeling and Analysis of Timed Systems (FORMATS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9268))

Abstract

Industrial applications usually require safety and stability properties. The safety property guarantees that “something bad” never happens, and the stability property guarantees that “something good” eventually happens. The analyses of both properties are usually performed in isolation. In this work, we consider analyzing both properties by a single automatic approach for hybrid systems. We basically merge analyses of both properties to exploit the knowledge gained from the analysis of each of them in the analysis of the other. We show how both analyses can be divided into multiple steps and interlocked such that both benefit from each other. In fact, we compute single-mode Lyapunov functions, unroll the hybrid system’s automaton via repeated reachability queries, and, finally, compute a global Lyapunov function. Each reachability query is simplified by exploiting the knowledge gained from the single-mode Lyapunov functions. The final computation of the global Lyapunov function is simplified by a precise characterization of the reachable states and reuses the single-mode Lyapunov functions.

We provide automated tools necessary to link the analyses and report on promising experiments we performed using our new prototype tool.

This work has been partly supported by the German Research Foundation (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS, www.avacs.org).

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Authors and Affiliations

  1. Carl von Ossietzky University of Oldenburg, 26111, Oldenburg, Germany

    Eike Möhlmann, Willem Hagemann & Oliver Theel

Authors
  1. Eike Möhlmann
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  2. Willem Hagemann
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  3. Oliver Theel
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Corresponding author

Correspondence to Eike Möhlmann .

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Editors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    Sriram Sankaranarayanan

  2. University of Florence, Florence, Italy

    Enrico Vicario

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Möhlmann, E., Hagemann, W., Theel, O. (2015). Hybrid Tools for Hybrid Systems – Proving Stability and Safety at Once. In: Sankaranarayanan, S., Vicario, E. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2015. Lecture Notes in Computer Science(), vol 9268. Springer, Cham. https://doi.org/10.1007/978-3-319-22975-1_15

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  • DOI: https://doi.org/10.1007/978-3-319-22975-1_15

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  • Online ISBN: 978-3-319-22975-1

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