Software & Systems Modeling

, Volume 18, Issue 3, pp 1613–1636 | Cite as

Rigorous design of cyber-physical systems

Linking physicality and computation
  • Simon BliudzeEmail author
  • Sébastien Furic
  • Joseph Sifakis
  • Antoine Viel
Theme Section Paper


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.


Cyber-physical systems design Structural equational modeling Modelica Linear graphs Bond graphs Idealization Abstraction Hybrid dataflow networks Discretization Language embedding 


  1. 1.
    Alur, R.: Principles of Cyber-Physical Systems. MIT Press, Cambridge (2015)Google Scholar
  2. 2.
    Ascher, U.M., Chin, H., Petzold, L.R., Reich, S.: Stabilization of constrained mechanical systems with DAEs and invariant manifolds. Mech. Struct. Mach. 23(2), 135–157 (1995). MathSciNetCrossRefGoogle Scholar
  3. 3.
    Basu, A., Bozga, M., Sifakis, J.: Modeling heterogeneous real-time components in BIP. In: 4th IEEE International Conference on Software Engineering and Formal Methods (SEFM06), invited talk, pp. 3–12 (2006).
  4. 4.
    Basu, A., Bensalem, S., Bozga, M., Combaz, J., Jaber, M., Nguyen, T.H., Sifakis, J.: Rigorous component-based system design using the BIP framework. IEEE Softw. 28(3), 41–48 (2011). CrossRefGoogle Scholar
  5. 5.
    Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1, 1–16 (1972). MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Benveniste, A., Caspi, P., Edwards, S.A., Halbwachs, N., Guernic, P.L., de Simone, R.: The synchronous languages twelve years later. Proc. IEEE, Spec. Issue Embed. Syst. 91(1), 64–83 (2003)Google Scholar
  7. 7.
    Benveniste, A., Bourke, T., Caillaud, B., Pouzet, M.: Non-standard semantics of hybrid systems modelers. J. Comput. Syst. Sci. 78, 877–910 (2012). MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Benveniste, A., Bourke, T., Caillaud, B., Pouzet, M.: Hybrid systems modeling challenges caused by cyber-physical systems. In: Baras, J., Srinivasan, V. (eds) Cyber-Physical Systems (CPS) Foundations and Challenges. Available on-line: (2013) (to appear)
  9. 9.
    Berger, C., Mousavi, M.R., (eds): Cyber Physical Systems. Design, Modeling, and Evaluation—5th International Workshop, CyPhy 2015, Amsterdam, The Netherlands, 8 Oct 2015. Proceedings, Lecture Notes in Computer Science, vol. 9361, Springer (2015).
  10. 10.
    Bliudze, S., Furic, S.: An operational semantics for hybrid systems involving behavioral abstraction. In: Proceedings of the 10th International Modelica Conference, Linköping University Electronic Press, Linköpings Universitet, Linköping, Linköping Electronic Conference Proceedings, pp. 693–706 (2014).
  11. 11.
    Bliudze, S., Krob, D.: Modelling of complex systems: systems as dataflow machines. Fundam. Inf. 91, 1–24 (2009). MathSciNetzbMATHGoogle Scholar
  12. 12.
    Bliudze, S., Sifakis, J.: The algebra of connectors—structuring interaction in BIP. In: Proceedings of the EMSOFT’07, ACM SigBED, Salzburg, Austria, pp. 11–20 (2007)Google Scholar
  13. 13.
    Blochwitz, T., Otter, M., Arnold, M., Bausch, C., Elmqvist, H., Junghanns, A., Mauß, J., Monteiro, M., Neidhold, T., Neumerkel, D., Olsson, H., Peetz, J.V., Wolf, S., Clauß, C.: The functional mockup interface for tool independent exchange of simulation models. In: Proceedings of the 8th International Modelica Conference, Linköping University Electronic Press, vol. 63, pp. 105–114 (2011)Google Scholar
  14. 14.
    Bornot, S., Sifakis, J.: An algebraic framework for urgency. Inf. Comput. 163(1), 172–202 (2000). MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Bozga, M.D., Sfyrla, V., Sifakis, J.: Modeling synchronous systems in BIP. In: Proceedings of the Seventh ACM International Conference on Embedded Software, ACM, New York, NY, USA, EMSOFT ’09, pp. 77–86 (2009).
  16. 16.
    Broman, D., Brooks, C., Greenberg, L., Lee, E.A., Masin, M., Tripakis, S., Wetter, M.: Determinate composition of FMUs for co-simulation. In: Proceedings of the Eleventh ACM International Conference on Embedded Software, IEEE Press, Piscataway, NJ, USA, EMSOFT ’13, pp. 2:1–2:12 (2013). URL
  17. 17.
    Caspi, P., Pilaud, D., Halbwachs, N., Plaice, J.: Lustre: a declarative language for programming synchronous systems. In: Conference Record of the Fourteenth Annual ACM Symposium on Principles of Programming Languages, Munich, Germany, 21–23 Jan 1987. ACM Press, pp. 178–188 (1987).
  18. 18.
    Cellier, F.E., Kofman, E.: Continuous System Simulation. Springer, Berlin (2006)zbMATHGoogle Scholar
  19. 19.
    Cellier, F.E., Kofman, E., Migoni, G., Bortolotto, M.: Quantized state system simulation. In: Proceedings of Grand Challenges in Modeling and Simulation (GCMS08), pp. 504–510 (2008)Google Scholar
  20. 20.
    Dabney, J.B., Harman, T.L.: Mastering Simulink. Prentice Hall, Upper Saddle River (2004)Google Scholar
  21. 21.
    Derler, P., Lee, E.A., Sangiovanni-Vincentelli, A.L.: Modeling cyber-physical systems. Proc. IEEE 100(1), 13–28 (2012). CrossRefGoogle Scholar
  22. 22.
    Fitzgerald, J., Gamble, C., Larseny, P.G., Pierce, K., Woodcock, J.: Cyber-physical systems design: formal foundations, methods and integrated tool chains. In: 2015 IEEE/ACM 3rd FME Workshop on Formal Methods in Software Engineering (FormaliSE), pp. 40–46 (2015).
  23. 23.
    Fritzson, P.: Introduction to Modeling and Simulation of Technical and Physical Systems with Modelica. Wiley, Hoboken (2011)CrossRefGoogle Scholar
  24. 24.
    Furic, S.: Connection semantics: overview of some classical approaches and proposal for a novel one. (unpublished, available on demand) (2013)Google Scholar
  25. 25.
    Furic, S.: Physical connection proposal for the FMI. Technical Report, FMI Design Meeting, 9–10 Feb 2015, DLR, Germany (2015a)Google Scholar
  26. 26.
    Furic, S.: A physical connection proposal for the FMI. In: Workshop Sim@SL, ENS Cachan, Paris (2015b)Google Scholar
  27. 27.
    Gear, C.W.: Automatic multirate methods for ordinary differential equations. Technical Report, UIUCDS-R-80-1000, Illinois University, Urbana (USA) (1980)Google Scholar
  28. 28.
    Geisberger, E., Broy, M., (eds): Living in a Networked World: Integrated Research Agenda Cyber-Physical Systems (agendaCPS). acatech STUDIE, Utz Verlag GmbH (2015)Google Scholar
  29. 29.
    Henzinger, T.A.: The Theory of Hybrid Automata. Springer, Berlin (2000)CrossRefzbMATHGoogle Scholar
  30. 30.
    Hogan, N., Breedveld, P.: Chapter 15: the physical basis of analogies in network models of physical system dynamics. In: Bishop, R.H. (ed.) The Mechatronics Handbook, pp. 1–10. CRC Press, Boca Raton (2002)Google Scholar
  31. 31.
    Karnopp, D.C., Margolis, D.L., Rosenberg, R.C.: System Dynamics: Modeling, Simulation, and Control of Mechatronic Systems, 5th edn. Wiley, Hoboken (2012)CrossRefGoogle Scholar
  32. 32.
    Konečný, M., Taha, W., Bartha, F.A., Duracz, J., Duracz, A., Ames, A.D.: Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point. Nonlinear Anal. Hybrid Syst. 20, 1–20 (2016). MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Kübler, R., Schiehlen, W.: Two methods of simulator coupling. Math. Comput. Model. Dyn. Syst. 6(2), 93–113 (2000)CrossRefzbMATHGoogle Scholar
  34. 34.
    Lamb, J.D., Asher, G.M., Woodall, D.R.: Network realisation of bond graphs. In: Granada, J.J., Cellier, F.E. (eds.) Proceedings of International Conference on Bond Graph Modeling (ICBGM ’93), Society for Computer Simulation, Simulation Series, vol. 25(2), pp. 85–90 (1993)Google Scholar
  35. 35.
    Lee, E.A.: Cyber physical systems: design challenges. In: 2008 11th IEEE International Symposium on Object Oriented Real-Time Distributed Computing (ISORC), pp. 363–369 (2008).
  36. 36.
    Lee, E.A.: Constructive models of discrete and continuous physical phenomena. IEEE Access 2, 797–821 (2014). CrossRefGoogle Scholar
  37. 37.
    Lee, E.A., Zheng, H.: Operational semantics of hybrid systems. In: Morari, M., Thiele, L. (eds.) Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, vol. 3414, Springer, Heidelberg, pp. 25–53 (2005).
  38. 38.
    Lelarasmee, E., Ruehli, A., Sangiovanni-Vincentelli, A.L.: The waveform relaxation method for time-domain analysis of large scale integrated circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 1(3), 131–145 (1982). CrossRefGoogle Scholar
  39. 39.
    Lindstrøm, T.: An invitation to nonstandard analysis. In: Cutland, N. (ed.) Nonstandard Analysis and its Applications, No. 10 in London Mathematical Society Student Texts, Cambridge University Press (1988)Google Scholar
  40. 40.
    Matsikoudis, E., Lee, E.A.: On fixed points of strictly causal functions. In: Formal Modeling and Analysis of Timed Systems, Springer, pp. 183–197 (2013)Google Scholar
  41. 41.
    Mattsson, S.E., Olsson, H., Elmqvist, H.: Dynamic Selection of states in Dymola. In: Proceedings of Modelica Workshop 2000, Lund, pp. 61–67 (2000)Google Scholar
  42. 42.
    Perelson, A.S., Oster, G.F.: Bond graphs and linear graphs. J Frankl. Inst. 302(2), 159–185 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Rajkumar, R.R., Lee, I., Sha, L., Stankovic, J. Cyber-physical systems: the next computing revolution. In: Proceedings of the 47th Design Automation Conference, ACM, New York, NY, USA, DAC ’10, pp. 731–736 (2010).
  44. 44.
    Robinson, A.: Non Standard Analysis. North Holland, Amsterdam (1966)zbMATHGoogle Scholar
  45. 45.
    Rust, H.: Operational semantics for timed systems: a non-standard approach to uniform modeling of timed and hybrid systems. Lecture Notes in Computer Science, vol. 3456. Springer (2005).
  46. 46.
    Sfyrla, V., Tsiligiannis, G., Safaka, I., Bozga, M., Sifakis, J.: Compositional translation of simulink models into synchronous BIP. In: 2010 International Symposium on Industrial Embedded Systems (SIES), pp. 217–220 (2010). (2010)
  47. 47.
    Sifakis, J.: System design automation: challenges and limitations. Proc. IEEE 103(11), 2093–2103 (2015). CrossRefGoogle Scholar
  48. 48.
    Sztipanovits, J., Bapty, T., Neema, S., Koutsoukos, X., Jackson, E.: Design tool chain for cyber-physical systems: Lessons learned. In: Design Automation Conference (DAC), 2015 52nd ACM/EDAC/IEEE, pp. 1–6 (2015),
  49. 49.
    Tellegen, B.D.: A general network theorem, with applications. Philips Res. Rep. 7(4), 259–269 (1952)MathSciNetzbMATHGoogle Scholar
  50. 50.
    Trent, H.M.: Isomorphisms between oriented linear graphs and lumped physical systems. J. Acoust.l Soc. Am. 27(3), 500–527 (1955)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Tripakis, S.: Bridging the semantic gap between heterogeneous modeling formalisms and FMI. In: 2015 International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation (SAMOS), IEEE, pp. 60–69 (2015)Google Scholar
  52. 52.
    Vladimirescu, A.: The SPICE Book. Wiley, Hoboken (1993)Google Scholar
  53. 53.
    Walther, M., Waurich, V., Schubert, C., Dr-Ing GubschBliudze, I.: Equation based parallelization of modelica models. In: Proceedings of the 10th International Modelica Conference, Linköping University Electronic Press, Linköpings Universitet, Linköping, Linköping Electronic Conference Proceedings, pp. 1213–1220, (2014).
  54. 54.
    Wolf, W.: Cyber-physical systems. Computer 42(3), 88–89 (2009). CrossRefGoogle Scholar
  55. 55.
    Zeigler, B.P., Lee, J.S.: Theory of quantized systems: formal basis for DEVS/HLA distributed simulation environment. SPIE Proc. 3369, 49–58 (1998)CrossRefGoogle Scholar
  56. 56.
    Zheng, H., Lee, E.A., Ames, A.D.: Beyond zeno: get on with It! In: Hespanha, J.P., Tiwari, A.: (eds). Hybrid Systems: Computation and Control, 9th International Workshop, HSCC 2006, Santa Barbara, CA, USA, 29–31 March 2006. Proceedings, Springer, Berlin, pp. 568–582 (2006).

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.INRIA Lille – Nord EuropeVilleneuve d’AscqFrance
  2. 2.INRIA Centre de ParisParisFrance
  3. 3.Verimag, Bâtiment IMAGSaint Martin d’HèresFrance
  4. 4.Siemens Industry Software SASRoanneFrance

Personalised recommendations