Abstract
Co-simulation is a technique to orchestrate multiple simulators in order to approximate the behavior of a coupled system as a whole. Simulators execute in a lockstep fashion, each exchanging inputs and output data points with the other simulators at pre-accorded times.
In the context of systems with a physical and a cyber part, the communication frequency with which the simulators of each part communicate can have a negative impact in the accuracy of the global simulation results. In fact, the computed behavior can be qualitatively different, compared to the actual behavior of the original system, laying waste to potentially many hours of computation. It is therefore important to develop methods that answer whether a given communication frequency guarantees trustworthy co-simulation results.
In this paper, we take a small step in that direction. We develop a technique to approximate the lowest frequency for which a particular set of simulation tools can exchange values in a co-simulation and obtain results that can be trusted.
This work has been done 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 Ph.D. fellowship grants from the Agency for Innovation by Science and Technology in Flanders (IWT, dossier 151067).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Arnold, M.: Stability of sequential modular time integration methods for coupled multibody system models. J. Comput. Nonlinear Dyn. 5(3), 9 (2010)
Bertsch, C., Ahle, E., Schulmeister, U.: The Functional Mockup Interface-seen from an industrial perspective. In: 10th International Modelica Conference (2014)
Blockwitz, T., Otter, M., Akesson, J., Arnold, M., Clauss, C., Elmqvist, H., Friedrich, M., Junghanns, A., Mauss, J., Neumerkel, D., Olsson, H., Viel, A.: Functional Mockup Interface 2.0: the standard for tool independent exchange of simulation models. In: 9th International Modelica Conference, pp. 173–184. Linköping University Electronic Press, Munich, November 2012
Branicky, M.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)
Busch, M.: Continuous approximation techniques for co-simulation methods: analysis of numerical stability and local error. ZAMM - J. Appl. Math. Mech. 96(9), 1061–1081 (2016)
Cellier, F.E., Kofman, E.: Continuous System Simulation. Springer Science & Business Media, New York (2006). https://doi.org/10.1007/0-387-30260-3
Cremona, F., Lohstroh, M., Broman, D., Di Natale, M., Lee, E.A., Tripakis, S.: Step revision in hybrid co-simulation with FMI. In: 14th ACM-IEEE International Conference on formal Methods and Models for System Design, Kanpur, India (2016)
Friedman, J., Ghidella, J.: Using model-based design for automotive systems engineering - requirements analysis of the power window example. SAE Technical Paper, April 2006
Goebel, R., Sanfelice, R.G., Teel, A.R.: Hybrid Dynamical Systems: Modeling, Stability and Robustness. Princeton University Press, Princeton (2012)
Gomes, C., Thule, C., Broman, D., Larsen, P.G., Vangheluwe, H.: Co-simulation: state of the art. Technical report, February 2017. arXiv:1702.00686
Kalmar-Nagy, T., Stanciulescu, I.: Can complex systems really be simulated? Appl. Math. Comput. 227, 199–211 (2014)
Karalis, P., Navarro-López, E.M.: Feedback stability for dissipative switched systems. In: Proceedings of 20th IFAC World Congress. IFAC, Toulouse (2017, to appear)
Khalil, H.K.: Nonlinear Systems. Prentice-Hall, Upper Saddle River (1996)
Liberzon, D.: Switching in Systems and Control. Springer Science & Business Media, Boston (2012). https://doi.org/10.1007/978-1-4612-0017-8
Lygeros, J., Johansson, K., Simic, S., Zhang, J., Sastry, S.: Dynamical properties of hybrid automata. IEEE Trans. Autom. Control 48(1), 2–17 (2003)
Lygeros, J.: Lecture notes on hybrid systems (2004). https://robotics.eecs.berkeley.edu/~sastry/ee291e/lygeros.pdf
Mitra, S., Liberzon, D., Lynch, N.: Verifying average dwell time of hybrid systems. ACM Trans. Embed. Comput. Syst. 8(1), 1–37 (2008)
Navarro-López, E.M., Carter, R.: Hybrid automata: an insight into the discrete abstraction of discontinuous systems. Int. J. Syst. Sci. 42(11), 1883–1898 (2011)
Navarro-López, E.M., Carter, R.: Deadness and how to disprove liveness in hybrid dynamical systems. Theoret. Comput. Sci. 642, 1–23 (2016)
Navarro-López, E.M., Laila, D.S.: Group and total dissipativity and stability of multi-equilibria hybrid automata. IEEE Trans. Autom. Control 58(12), 3196–3202 (2013)
Ni, Y., Broenink, J.F.: Hybrid systems modelling and simulation in DESTECS: a co-simulation approach. In: Klumpp, M. (ed.) 26th European Simulation and Modelling Conference, pp. 32–36. EUROSIS-ETI, Ghent (2012)
Nielsen, C.B., Larsen, P.G., Fitzgerald, J., Woodcock, J., Peleska, J.: Systems of systems engineering: basic concepts, model-based techniques, and research directions. ACM Comput. Surv. 48(2), 18:1–18:41 (2015)
Schweizer, B., Li, P., Lu, D.: Explicit and implicit cosimulation methods: stability and convergence analysis for different solver coupling approaches. J. Comput. Nonlinear Dyn. 10(5), 051007 (2015)
Tomiyama, T., D’Amelio, V., Urbanic, J., ElMaraghy, W.: Complexity of multi-disciplinary design. CIRP Ann. - Manuf. Technol. 56(1), 185–188 (2007)
Van der Auweraer, H., Anthonis, J., De Bruyne, S., Leuridan, J.: Virtual engineering at work: the challenges for designing mechatronic products. Eng. Comput. 29(3), 389–408 (2013)
Vangheluwe, H., De Lara, J., Mosterman, P.J.: An introduction to multi-paradigm modelling and simulation. In: AI, Simulation and Planning in High Autonomy Systems, pp. 9–20. SCS (2002)
Zhang, F., Yeddanapudi, M., Mosterman, P.: Zero-crossing location and detection algorithms for hybrid system simulation. In: IFAC World Congress, pp. 7967–7972 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Gomes, C., Karalis, P., Navarro-López, E.M., Vangheluwe, H. (2018). Approximated Stability Analysis of Bi-modal Hybrid Co-simulation Scenarios. In: Cerone, A., Roveri, M. (eds) Software Engineering and Formal Methods. SEFM 2017. Lecture Notes in Computer Science(), vol 10729. Springer, Cham. https://doi.org/10.1007/978-3-319-74781-1_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-74781-1_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-74780-4
Online ISBN: 978-3-319-74781-1
eBook Packages: Computer ScienceComputer Science (R0)