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Rigorous design of cyber-physical systems

Linking physicality and computation

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Abstract

Cyber-physical systems have developed into a very active research field, with a broad range of challenges and research directions going from requirements, to implementation and simulation, as well as validation and verification to guarantee essential properties. In this survey paper, we focus exclusively on the following fundamental issue: how to link physicality and computation, continuous time-space dynamics with discrete untimed ones? We consider that cyber-physical system design flow involves the following three main steps: (1) cyber-physical systems modeling; (2) discretization for executability; and (3) simulation and implementation. We review—and strive to provide insight into possible approaches for addressing—the key issues, for each of these three steps.

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Notes

  1. For this reason, approaches to physical system modeling based on these analogies are often termed energetic approaches.

  2. In this short introduction to linear graphs, we will not consider transducers for the sake of simplicity. The interested reader can refer to any decent book about linear graphs for more information about transducers.

  3. Analytical integration is generally not practicable in real-world applications, for performance reasons and also because tools cannot often be given a symbolic version of equations to be solved.

  4. This is of course not possible for any equation in general. More elaborated techniques (including some fix point determination) will be needed in case inversion is not possible by means of simple symbolic manipulations.

  5. As in the case of linear graphs, we will not consider transducers in this short presentation of bond graphs. Again, we advise the interested reader to refer to any decent book about bond graphs for more information.

  6. The noteworthy symmetry between both recipes reflects the duality property of efforts and flows in the underlying physical model [30]. In contrast, linear graphs do not enjoy such a symmetry.

  7. Causality analysis [31] can also be used to obtain executable models directly from the bond graph structure. However, this technique has been superseded in most industrial tools by the more modern matching approaches which are more general (they don’t require the initial model to be a bond graph) and more efficient (they achieve polynomial time performance in the worst case).

  8. They are actually “virtual measurement points” according to the common interpretation of linear graphs following Trent [50].

  9. This is a necessary condition for executability.

  10. In Sect. 2.1.4, we used these results to build the model based on bond graphs.

  11. Although several distinct definitions of the notion of index exist in the literature, they all reflect the “distance” between a system of DAEs and the corresponding system of ODEs.

  12. It can be shown that this is also the case for vx with respect to vy, see Mattsson et al. [41] for a complete discussion.

  13. Undetected at compilation time according to Modelica semantics which only impose restrictions over the number of independent equations (determined based on syntax considerations). Here, the model is found to have two degrees of freedom, we should then be able to reinitialize two state variables on discrete event instants.

  14. A careful reader may have noticed that the actual value of e has no influence on the numerical solution, at least theoretically. In practice, however, numerical conditioning issues arise as a consequence of finite precision of computer arithmetic.

  15. http://www-verimag.imag.fr/Rigorous-Design-of-Component-Based.html.

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Authors and Affiliations

  1. INRIA Lille – Nord Europe, Parc scientifique de la Haute Borne, 40 avenue Halley, 59650, Villeneuve d’Ascq, France

    Simon Bliudze

  2. INRIA Centre de Paris, 2 rue Simone Iff, 75589, Paris, France

    Sébastien Furic

  3. Verimag, Bâtiment IMAG, 700, avenue centrale, 38401, Saint Martin d’Hères, France

    Joseph Sifakis

  4. Siemens Industry Software SAS, 14 Boulevard de Valmy, 42300, Roanne, France

    Antoine Viel

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  1. Simon Bliudze
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  2. Sébastien Furic
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  4. Antoine Viel
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Correspondence to Simon Bliudze.

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Communicated by Prof. J. Sztipanovits, M. Broy, and H. Daembkes.

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Bliudze, S., Furic, S., Sifakis, J. et al. Rigorous design of cyber-physical systems. Softw Syst Model 18, 1613–1636 (2019). https://doi.org/10.1007/s10270-017-0642-5

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