Hybrid automata: from verification to implementation

  • Stanley Bak
  • Omar Ali Beg
  • Sergiy Bogomolov
  • Taylor T. Johnson
  • Luan Viet Nguyen
  • Christian Schilling
Regular Paper


Hybrid automata are an important formalism for modeling dynamical systems exhibiting mixed discrete–continuous behavior such as control systems and are amenable to formal verification. However, hybrid automata lack expressiveness compared to integrated model-based design frameworks such as the MathWorks’ Simulink/Stateflow (SlSf). In this paper, we propose a technique for correct-by-construction compositional design of cyber-physical systems (CPS) by embedding hybrid automata into SlSf models. Hybrid automata are first verified using verification tools such as SpaceEx and then automatically translated to embed the hybrid automata into SlSf models such that the properties verified are transferred and maintained in the translated SlSf model. The resultant SlSf model can then be used for automatic code generation and deployment to hardware, resulting in an implementation. The approach is implemented in a software tool building on the HyST model transformation tool for hybrid systems. We show the effectiveness of our approach on a CPS case study—a closed-loop buck converter—and validate the overall correct-by-construction methodology: from formal verification to implementation in hardware controlling an actual physical plant.


Hybrid automata Model-based design Simulink/Stateflow 



The authors thank the anonymous reviewers for their insightful comments. The material presented in this paper is based upon work supported by the Air Force Office of Scientific Research (AFOSR), in part under contract numbers FA9550-15-1-0258 and W911NF-16-1-0534, by AFRL through contract number FA8750-15-1-0105, by the National Science Foundation (NSF) under Grant Numbers CNS 1464311, EPCN 1509804, and CCF 1527398, and by the ARC Project DP140104219 “Robust AI Planning for Hybrid Systems”. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of AFRL, AFOSR, or NSF.


  1. 1.
    Agrawal, A., Simon, G., Karsai, G.: Semantic translation of Simulink/Stateflow models to hybrid automata using graph transformations. Electr. Notes Theor. Comput. Sci 109, 43–56 (2004). doi: 10.1016/j.entcs.2004.02.055 CrossRefzbMATHGoogle Scholar
  2. 2.
    Agut, D.E.N., van Beek, D.A., Rooda, J.E.: Syntax and semantics of the compositional interchange format for hybrid systems. J. Log. Algebr. Program 82(1), 1–52 (2013). doi: 10.1016/j.jlap.2012.07.001 MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Alur, R., Kanade, A., Ramesh, S., Shashidhar, K.C.: Symbolic analysis for improving simulation coverage of Simulink/Stateflow models. In: EMSOFT, pp. 89–98. ACM (2008). doi: 10.1145/1450058.1450071
  4. 4.
    Annpureddy, Y., Liu, C., Fainekos, G.E., Sankaranarayanan, S.: S-TaLiRo: a tool for temporal logic falsification for hybrid systems. In: TACAS, vol. 6605, pp. 254–257. Springer (2011). doi: 10.1007/978-3-642-19835-9_21
  5. 5.
    Bak, S., Bogomolov, S., Johnson, T.T.: HYST: a source transformation and translation tool for hybrid automaton models. In: HSCC, pp. 128–133, ACM (2015). doi: 10.1145/2728606.2728630
  6. 6.
    Bak, S., Johnson, T.T.: Periodically-scheduled controller analysis using hybrid systems reachability and continuization. In: RTSS, pp. 195–205. IEEE Computer Society (2015). doi: 10.1109/RTSS.2015.26
  7. 7.
    Balasubramanian, D., Pasareanu, C.S., Whalen, M.W., Karsai, G., Lowry, M.R.: Polyglot: modeling and analysis for multiple statechart formalisms. In: ISSTA, pp. 45–55. ACM (2011), doi: 10.1145/2001420.2001427
  8. 8.
    Bogomolov, S., Donzé, A., Frehse, G., Grosu, R., Johnson, T.T., Ladan, H., Podelski, A., Wehrle, M.: Guided search for hybrid systems based on coarse-grained space abstractions. STTT 18(4), 449–467 (2016). doi: 10.1007/s10009-015-0393-y CrossRefGoogle Scholar
  9. 9.
    Bogomolov, S., Frehse, G., Greitschus, M., Grosu, R., Pasareanu, C.S., Podelski, A., Strump, T.: Assume-guarantee abstraction refinement meets hybrid systems. In: HVC. LNCS, vol. 8855, pp. 116–131. Springer (2014). doi: 10.1007/978-3-319-13338-6_10
  10. 10.
    Bogomolov, S., Frehse, G., Grosu, R., Ladan, H., Podelski, A., Wehrle, M.: A box-based distance between regions for guiding the reachability analysis of SpaceEx. In: CAV. LNCS, vol. 7358, pp. 479–494. Springer (2012). doi: 10.1007/978-3-642-31424-7_35
  11. 11.
    Bogomolov, S., Schilling, C., Bartocci, E., Batt, G., Kong, H., Grosu, R.: Abstraction-based parameter synthesis for multiaffine systems. In: HVC. LNCS, vol. 9434, pp. 19–35. Springer (2015). doi: 10.1007/978-3-319-26287-1_2
  12. 12.
    Bouissou, O., Chapoutot, A.: An operational semantics for Simulink’s simulation engine. In: LCTES, pp. 129–138. ACM (2012). doi: 10.1145/2248418.2248437
  13. 13.
    Carloni, L., Di Benedetto, M.D., Pinto, A., Sangiovanni-Vincentelli, A.: Modeling techniques, programming languages, design toolsets and interchange formats for hybrid systems. Tech. Rep. (2004)Google Scholar
  14. 14.
    Carloni, L.P., Passerone, R., Pinto, A., Sangiovanni-Vincentelli, A.L.: Languages and tools for hybrid systems design. In: Foundations and Trends in Electronic Design Automation 1(1/2) (2006). doi: 10.1561/1000000001
  15. 15.
    Chen, M., Ravn, A.P., Wang, S., Yang, M., Zhan, N.: A two-way path between formal and informal design of embedded systems. In: UTP. LNCS, vol. 10134, pp. 65–92. Springer (2016)Google Scholar
  16. 16.
    Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: CAV. LNCS, vol. 8044, pp. 258–263. Springer (2013). doi: 10.1007/978-3-642-39799-8_18
  17. 17.
    Clarke, E.M., Zuliani, P.: Statistical model checking for cyber-physical systems. In: ATVA. LNCS, vol. 6996, pp. 1–12. Springer (2011). doi: 10.1007/978-3-642-24372-1_1
  18. 18.
    Donzé, A.: Breach, a toolbox for verification and parameter synthesis of hybrid systems. In: CAV. LNCS, vol. 6174, pp. 167–170. Springer (2010). doi: 10.1007/978-3-642-14295-6_17
  19. 19.
    Duggirala, P.S., Mitra, S., Viswanathan, M.: Verification of annotated models from executions. In: EMSOFT, pp. 26:1–26:10. IEEE (2013). doi: 10.1109/EMSOFT.2013.6658604
  20. 20.
    Fisher, M.E.: A semiclosed-loop algorithm for the control of blood glucose levels in diabetics. IEEE Trans. Biomed. Eng. 38(1), 57–61 (1991)CrossRefGoogle Scholar
  21. 21.
    Frehse, G., Guernic, C.L., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV. LNCS, vol. 6806, pp. 379–395. Springer (2011). doi: 10.1007/978-3-642-22110-1_30
  22. 22.
    Hamon, G.: A denotational semantics for Stateflow. In: EMSOFT, pp. 164–172. ACM (2005). doi: 10.1145/1086228.1086260
  23. 23.
    Hamon, G., Rushby, J.M.: An operational semantics for Stateflow. STTT 9(5–6), 447–456 (2007). doi: 10.1007/s10009-007-0049-7 CrossRefzbMATHGoogle Scholar
  24. 24.
    Hybrid Automata: From verification to implementation—supplementary material.
  25. 25.
    Jiang, Z., Pajic, M., Alur, R., Mangharam, R.: Closed-loop verification of medical devices with model abstraction and refinement. STTT 16(2), 191–213 (2014). doi: 10.1007/s10009-013-0289-7 CrossRefGoogle Scholar
  26. 26.
    Johansson, K.H., Egerstedt, M., Lygeros, J., Sastry, S.: On the regularization of zeno hybrid automata. Syst. Control Lett. 38(3), 141–150 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. STTT 1(1–2), 134–152 (1997). doi: 10.1007/s100090050010 CrossRefzbMATHGoogle Scholar
  28. 28.
    Lavalle, S.M., Kuffner, J.J., Jr.: Rapidly-exploring random trees: progress and prospects. In: Donald, B., Lynch, K., Rus, D. (eds.) Algorithmic and Computational Robotics: New Directions, pp. 293–308. A K Peters/CRC Press (2000)Google Scholar
  29. 29.
    Manamcheri, K., Mitra, S., Bak, S., Caccamo, M.: A step towards verification and synthesis from Simulink/Stateflow models. In: Proceedings of the 14th international conference on Hybrid systems: computation and control HSCC’11, pp. 317–318. ACM (2011). doi: 10.1145/1967701.1967749
  30. 30.
    Minopoli, S., Frehse, G.: From simulation models to hybrid automata using urgency and relaxation. In: HSCC, pp. 287–296. ACM (2016). doi: 10.1145/2883817.2883825
  31. 31.
    Minopoli, S., Frehse, G.: SL2SX translator: from Simulink to SpaceEx models. In: HSCC, pp. 93–98. ACM (2016). doi: 10.1145/2883817.2883826
  32. 32.
    Nguyen, L.V., Johnson, T.T.: Benchmark: DC-to-DC switched-mode power converters (buck converters, boost converters, and buck-boost converters). In: ARCH. EPiC Series in Computing, vol. 34, pp. 19–24. EasyChair (2014).
  33. 33.
    Pajic, M., Jiang, Z., Lee, I., Sokolsky, O., Mangharam, R.: From verification to implementation: a model translation tool and a pacemaker case study. In: RTAS, pp. 173–184. IEEE Computer Society (2012). doi: 10.1109/RTAS.2012.25
  34. 34.
    Pajic, M., Jiang, Z., Lee, I., Sokolsky, O., Mangharam, R.: Safety-critical medical device development using the UPP2SF model translation tool. ACM Trans. Embed. Comput. Syst. 13(4s), 127:1–127:26 (2014). doi: 10.1145/2584651
  35. 35.
    Pajic, M., Mangharam, R., Sokolsky, O., Arney, D., Goldman, J.M., Lee, I.: Model-driven safety analysis of closed-loop medical systems. IEEE Trans. Ind. Inform. 10(1), 3–16 (2014). doi: 10.1109/TII.2012.2226594 CrossRefGoogle Scholar
  36. 36.
    Pinto, A., Carloni, L.P., Passerone, R., Sangiovanni-Vincentelli, A.L.: Interchange format for hybrid systems: abstract semantics. In: HSCC. LNCS, vol. 3927, pp. 491–506. Springer (2006). doi: 10.1007/11730637_37
  37. 37.
    Pinto, A., Sangiovanni-Vincentelli, A.L., Carloni, L.P., Passerone, R.: Interchange formats for hybrid systems: review and proposal. In: HSCC. LNCS, vol. 3414, pp. 526–541. Springer (2005). doi: 10.1007/978-3-540-31954-2_34
  38. 38.
    Sampath, P., Rajeev, A.C., Ramesh, S.: Translation validation for Stateflow to C. In: DAC, pp. 23:1–23:6. ACM (2014). doi: 10.1145/2593069.2593237
  39. 39.
    Sanfelice, R.G., Copp, D.A., Nanez, P.: A toolbox for simulation of hybrid systems in Matlab/Simulink: hybrid equations (HyEQ) toolbox. In: HSCC, pp. 101–106. ACM (2013). doi: 10.1145/2461328.2461346
  40. 40.
    Schrammel, P., Jeannet, B.: From hybrid data-flow languages to hybrid automata: a complete translation. In: HSCC, pp. 167–176. ACM (2012). doi: 10.1145/2185632.2185658
  41. 41.
    Severns, R.P., Bloom, G.: Modern DC-to-DC Switchmode Power Converter Circuits. Van Nostrand Reinhold Company, New York (1985)CrossRefGoogle Scholar
  42. 42.
  43. 43.
    Tiwari, A., Shankar, N., Rushby, J.M.: Invisible formal methods for embedded control systems. Proc. IEEE 91(1), 29–39 (2003)CrossRefGoogle Scholar
  44. 44.
    Yan, G., Jiao, L., Li, Y., Wang, S., Zhan, N.: Approximate bisimulation and discretization of hybrid CSP. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A., (eds.) FM. LNCS, vol. 9995, pp. 702–720. Springer, Cham (2016) doi: 10.1007/978-3-319-48989-6_43
  45. 45.
    Zou, L., Zhan, N., Wang, S., Fränzle, M.: Formal verification of Simulink/Stateflow diagrams. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA. LNCS, vol. 9364, pp. 464–481. Springer, Cham (2015) doi: 10.1007/978-3-319-24953-7_33

Copyright information

© US Government (outside the USA) 2017

Authors and Affiliations

  • Stanley Bak
    • 1
  • Omar Ali Beg
    • 2
  • Sergiy Bogomolov
    • 3
  • Taylor T. Johnson
    • 4
  • Luan Viet Nguyen
    • 2
  • Christian Schilling
    • 5
  1. 1.Air Force Research LaboratoryDaytonUSA
  2. 2.University of Texas at ArlingtonArlingtonUSA
  3. 3.Australian National UniversityCanberraAustralia
  4. 4.Vanderbilt UniversityNashvilleUSA
  5. 5.University of FreiburgFreiburg im BreisgauGermany

Personalised recommendations