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A compositional modelling and analysis framework for stochastic hybrid systems

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Abstract

The theory of hybrid systems is well-established as a model for real-world systems consisting of continuous behaviour and discrete control. In practice, the behaviour of such systems is also subject to uncertainties, such as measurement errors, or is controlled by randomised algorithms. These aspects can be modelled and analysed using stochastic hybrid systems. In this paper, we present HModest, an extension to the Modest modelling language—which is originally designed for stochastic timed systems without complex continuous aspects—that adds differential equations and inclusions as an expressive way to describe the continuous system evolution. Modest is a high-level language inspired by classical process algebras, thus compositional modelling is an integral feature. We define the syntax and semantics of HModest and show that it is a conservative extension of Modest that retains the compositional modelling approach. To allow the analysis of HModest models, we report on the implementation of a connection to recently developed tools for the safety verification of stochastic hybrid systems, and illustrate the language and the tool support with a set of small, but instructive case studies.

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Notes

  1. Our implementation also supports fixed-size arrays and user-defined data structures, which are technical extensions but not conceptually relevant for this paper.

  2. Since we omitted the details of the expression syntax, we assume type correctness in assignments, guards, weights etc. instead of providing the (standard) type checking rules in detail.

  3. The semantics of par { ::Tank()::Controller() } itself contains additional locations because the two process calls are not syntactically equal to the behaviours of the processes called. The semantics shown above can be obtained as the semantics of the entire model by replacing the do construct in the Controller process by a (tail-)recursive process call and the call Tank() in the parallel composition by a direct call to TankOff().

  4. http://www.mono-poject.org/.

  5. Computations were performed on an AMD Athlon II X4 620 system with 4 GB RAM.

  6. Computations were performed on an Intel Core i7 860 system with 8 GB RAM.

  7. Computations were performed on an Intel Core i7 860 system with 8 GB RAM.

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Acknowledgements

The authors thank Pedro D’Argenio for discussions on the language design and Nicolás Wolovick (both from University of Cordoba, Argentina) for his support in the development of the concrete semantics.

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Authors and Affiliations

  1. Saarland University – Computer Science, Campus E1 3, 66123, Saarbrücken, Germany

    Ernst Moritz Hahn, Arnd Hartmanns & Holger Hermanns

  2. LS2: Software Modelling and Verification, RWTH Aachen University, 52056, Aachen, Germany

    Joost-Pieter Katoen

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  1. Ernst Moritz Hahn
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  2. Arnd Hartmanns
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  3. Holger Hermanns
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  4. Joost-Pieter Katoen
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Correspondence to Arnd Hartmanns.

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This work has been supported by the DFG as part of SFB/TR 14 AVACS, by the EU FP7 project MoVeS, by the DFG/NWO bilateral research project ROCKS and has received funding from the European Union Seventh Framework Programme under grant agreement number 295261 as part of the MEALS project.

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Hahn, E.M., Hartmanns, A., Hermanns, H. et al. A compositional modelling and analysis framework for stochastic hybrid systems. Form Methods Syst Des 43, 191–232 (2013). https://doi.org/10.1007/s10703-012-0167-z

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