Abstract
Engineering modern systems is becoming increasingly difficult due to the heterogeneity between different subsystems. Modelling and simulation techniques have traditionally been used to tackle complexity, but with increasing heterogeneity of the subsystems, it becomes impossible to find appropriate modelling languages and tools to specify and analyse the system as a whole.
Co-simulation is a technique to combine multiple models and their simulators in order to analyse the behaviour of the whole system over time. Past research, however, has shown that the naïve combination of simulators can easily lead to incorrect simulation results, especially when co-simulating hybrid systems.
This paper shows: (i) how co-simulation of a family of hybrid systems can fail to reproduce the order of events that should have occurred (event ordering); (ii) how to prove that a co-simulation algorithm is correct (w.r.t. event ordering), and if it is incorrect, how to obtain a counterexample; and (iii) how to correct an incorrect co-simulation algorithm. We apply the above method to two well known co-simulation algorithms used with the FMI Standard, and we show that one of them is incorrect for the family of hybrid systems under study, under the restrictions of the standard. The conclusion is that either the standard needs to be revised, or one of the algorithms should be avoided.
This work was started in the CAMPaM 2017 Workshop, executed under the framework of the COST Action IC1404 – Multi-Paradigm Modelling for Cyber-Physical Systems (MPM4CPS), and partially supported by: Flanders Make vzw, the strategic research centre for the manufacturing industry; and PhD fellowship grants from the Agency for Innovation by Science and Technology in Flanders (IWT, dossier 151067).
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Notes
- 1.
This formula assumes that the software FMU only outputs a timeout event after the timeout (as it happens in Fig. 7), and not at the timeout. In the latter case, the formula becomes \(P(H)=H \times N\).
- 2.
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Thule, C., Gomes, C., Deantoni, J., Larsen, P.G., Brauer, J., Vangheluwe, H. (2018). Towards the Verification of Hybrid Co-simulation Algorithms. In: Mazzara, M., Ober, I., Salaün, G. (eds) Software Technologies: Applications and Foundations. STAF 2018. Lecture Notes in Computer Science(), vol 11176. Springer, Cham. https://doi.org/10.1007/978-3-030-04771-9_1
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