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Abstractions Refinement for Hybrid Systems Diagnosability Analysis

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Diagnosability, Security and Safety of Hybrid Dynamic and Cyber-Physical Systems

Abstract

Hybrid systems are complex systems that combine both discrete and continuous behaviors. Verifying behavioral or safety properties of such systems, either at design stage such as state reachability, diagnosability, and predictability or on-line such as fault detection and isolation, is a challenging task. Actually, computing the reachable set of states of a hybrid system is an undecidable matter due to the infinite state space of continuous systems. One way to verify those properties over such systems is by computing discrete abstractions and inferring them from the abstract system back to the original system. In this chapter, we are concerned with abstractions oriented towards hybrid systems diagnosability checking. Our goal is to create discrete abstractions in order to verify, at design stage, if a fault that would occur at runtime could be unambiguously detected in finite time (or within a given finite time bound for bounded diagnosability) by the diagnoser. This verification can be done on the abstraction by classical methods developed for discrete event systems, which provide a counterexample in case of non-diagnosability. The absence of such a counterexample proves the diagnosability of the original hybrid system. In the presence of a counterexample, the first step is to check if it is not a spurious effect of the abstraction and actually exists for the hybrid system, witnessing thus non-diagnosability. Otherwise, we show how to refine the abstraction, guided by the elimination of the counterexample, and continue the process of looking for another counterexample until either a final result is obtained or we reach an inconclusive verdict. We make use of qualitative modeling and reasoning to compute discrete abstractions and we define several refinement strategies. Abstractions as timed automata are particularly studied as they allow one to handle time constraints that can be captured at a qualitative level from the hybrid system.

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Acknowledgements

The authors would like to thank Alban Grastien for his valuable comments and suggestions.

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Authors and Affiliations

  1. CEA, LIST, Laboratory of Model Driven Engineering for Embedded Systems, Gif-sur-Yvette, France

    Hadi Zaatiti & Jean-Pierre Gallois

  2. LRI, Univ. Paris-Sud & CNRS, Univ. Paris-Saclay, Gif-sur-Yvette, France

    Hadi Zaatiti, Lina Ye & Philippe Dague

  3. CentraleSupélec, Univ. Paris-Saclay, Gif-sur-Yvette, France

    Lina Ye

  4. LAAS-CNRS, Univ. de Toulouse, Toulouse, France

    Louise Travé-Massuyès

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  1. Hadi Zaatiti
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  2. Lina Ye
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  3. Philippe Dague
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  4. Jean-Pierre Gallois
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  5. Louise Travé-Massuyès
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Correspondence to Philippe Dague .

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  1. Institute Mines-Telecom Lille Douai, Douai, France

    Moamar Sayed-Mouchaweh

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Zaatiti, H., Ye, L., Dague, P., Gallois, JP., Travé-Massuyès, L. (2018). Abstractions Refinement for Hybrid Systems Diagnosability Analysis. In: Sayed-Mouchaweh, M. (eds) Diagnosability, Security and Safety of Hybrid Dynamic and Cyber-Physical Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-74962-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-74962-4_11

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