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Formally Verified Self-adaptation of an Incubator Digital Twin

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Abstract

The performance and reliability of Cyber-Physical Systems are increasingly aided through the use of digital twins, which mirror the static and dynamic behaviour of a Cyber-Physical System (CPS) in software. Digital twins enable the development of self-adaptive CPSs which reconfigure their behaviour in response to novel environments. It is crucial that these self-adaptations are formally verified at runtime, to avoid expensive re-certification of the reconfigured CPS. In this paper, we demonstrate formally verified self-adaptation in a digital twinning system, by constructing a non-deterministic model which captures the uncertainties in the system behaviour after a self-adaptation. We use Signal Temporal Logic to specify the safety requirements the system must satisfy after reconfiguration and employ formal methods based on verified monitoring over Flow* flowpipes to check these properties at runtime. This gives us a framework to predictively detect and mitigate unsafe self-adaptations before they can lead to unsafe states in the physical system.

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Notes

  1. 1.

    Flow* also has native support for time-varying interval uncertain parameters [12, Section 3.5], which may vary throughout the simulation leading to much greater uncertainty in the overall behaviour of the system over time.

  2. 2.

    https://docs.scipy.org/doc/scipy/index.html.

  3. 3.

    This notion is worth comparing this to notions of conformance between continuous and hybrid systems traces such as [19] and [3].

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Acknowledgements

Cláudio Gomes and Jim Woodcock are grateful to the Poul Due Jensen Foundation, which has supported the establishment of a new Centre for Digital Twin Technology at Aarhus University. Thomas Wright and Jim Woodcock gratefully acknowledge the support of the UK EPSRC for grant EP/V026801/1, UKRI Trustworthy Autonomous Systems Node in Verifiability. We also thank Jos Gibbons and Juliet Cooke for their feedback and suggestions on drafts of this paper as well as our anonymous reviewers for all of their valuable feedback which fed into the final version of the paper.

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  1. Department of Computer Science, University of York, Heslington, UK

    Thomas Wright & Jim Woodcock

  2. DIGIT, Department of Engineering, Aarhus University, Aarhus, Denmark

    Cláudio Gomes & Jim Woodcock

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  1. Thomas Wright
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  2. Cláudio Gomes
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  1. University of Limerick, CSIS and Lero, Limerick, Ireland

    Tiziana Margaria

  2. TU Dortmund, Dortmund, Germany

    Bernhard Steffen

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Wright, T., Gomes, C., Woodcock, J. (2022). Formally Verified Self-adaptation of an Incubator Digital Twin. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Practice. ISoLA 2022. Lecture Notes in Computer Science, vol 13704. Springer, Cham. https://doi.org/10.1007/978-3-031-19762-8_7

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