Skip to main content
SpringerLink
Log in

Current Challenges in the Verification of Hybrid Systems

  • Conference paper
  • First Online:
Cyber Physical Systems. Design, Modeling, and Evaluation (CyPhy 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9361))

Abstract

Latest developments brought interesting theoretical results and powerful tools for the reachability analysis of hybrid systems. However, there are still challenging problems to be solved in order to make those technologies applicable to large-scale applications in industrial context. To support this development, in this paper we give a brief overview of available algorithms and tools, and point out some of their individual characteristics regarding various properties which are crucial for the verification of hybrid systems. We present exemplary evaluations on three benchmarks to motivate the need for further development and discuss some of the main challenges for future research in this area.

This work was partially supported by the German Research Council (DFG) in the context of the HyPro project.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Althoff, M., Dolan, J.M.: Online verification of automated road vehicles using reachability analysis. IEEE Trans. Robot. 30(4), 903–918 (2014)

    Article  Google Scholar 

  2. Althoff, M., Frehse, G.: Benchmarks of the workshop on applied verification of continuous and hybrid systems (ARCH) (2014). http://cps-vo.org/group/ARCH/benchmarks

  3. Ames, A.D., Sastry, S.: Characterization of Zeno behavior in hybrid systems using homological methods. In: Proceedings of ACC 2005, pp. 1160–1165. IEEE Computer Society Press (2005)

    Google Scholar 

  4. Bak, S., Bogomolov, S., Johnson, T.T.: HYST: a source transformation and translation tool for hybrid automaton models. In: Proceedings of HSCC 2015, pp. 128–133. ACM (2015)

    Google Scholar 

  5. Barrett, C., Stump, A., Tinelli, C.: The satisfiability modulo theories library (SMT-LIB) (2010). http://www.SMT-LIB.org

  6. van Beek, D.A., Fokkink, W.J., Hendriks, D., Hofkamp, A., Markovski, J., van de Mortel-Fronczak, J.M., Reniers, M.A.: CIF 3: model-based engineering of supervisory controllers. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 575–580. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  7. Ben Makhlouf, I., Diab, H., Kowalewski, S.: Safety verification of a controlled cooperative platoon under loss of communication using zonotopes. In: Proceedings of ADHS 2012, pp. 333–338. IFAC-PapersOnLine (2012)

    Google Scholar 

  8. Benchmarks of continuous and hybrid systems. http://ths.rwth-aachen.de/research/hypro/benchmarks-of-continuous-and-hybrid-systems/

  9. Bujorianu, M., Lygeros, J.: Toward a general theory of stochastic hybrid systems. In: Blom, H.A.P., Lygeros, J. (eds.) Stochastic Hybrid Systems. LNCIS, vol. 337, pp. 3–30. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Chen, X.: Reachability Analysis of Non-Linear Hybrid Systems Using Taylor Models. Ph.D. thesis, RWTH Aachen University, Germany (2015)

    Google Scholar 

  11. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Taylor model flowpipe construction for non-linear hybrid systems. In: Proceedings of RTSS 2012, pp. 183–192. IEEE Computer Society Press (2012)

    Google Scholar 

  12. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  13. Collins, P., Bresolin, D., Geretti, L., Villa, T.: Computing the evolution of hybrid systems using rigorous function calculus. In: Proceedings of ADHS 2012, pp. 284–290. IFAC-PapersOnLine (2012)

    Google Scholar 

  14. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proceedings of SIGACT-SIGPLAN, pp. 84–96. ACM (1978)

    Google Scholar 

  15. Eggers, A.: Direct Handling of Ordinary Differential Equations in Constraint-solving-based Analysis of Hybrid Systems. Ph.D. thesis, Universität Oldenburg, Germany (2014)

    Google Scholar 

  16. Fehnker, A., Ivančić, F.: Benchmarks for hybrid systems verification. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004)

    Google Scholar 

  17. Fränzle, M., Herde, C., Ratschan, S., Schubert, T., Teige, T.: Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure. J. Satisf. Boolean Model. Comput. 1, 209–236 (2007)

    Google Scholar 

  18. Frehse, G., Kateja, R., Le Guernic, C.: Flowpipe approximation and clustering in space-time. In: Proceedings of HSCC 2013, pp. 203–212. ACM (2013)

    Google Scholar 

  19. Frehse, G.: Reachability of hybrid systems in space-time. In: Proceedings of EMSOFT 2015. ACM (2015)

    Google Scholar 

  20. Frehse, G., Le Guernic, C., 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 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  21. Fulton, N., Mitsch, S., Quesel, J.D., Völp, M., Platzer, A.: KeYmaera X: an axiomatic tactical theorem prover for hybrid systems. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS, vol. 9195, pp. 527–538. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  22. Gao, S., Kong, S., Clarke, E.M.: dReal: an SMT Solver for nonlinear theories over the reals. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 208–214. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  23. Henzinger, T.: The theory of hybrid automata. In: Proceedings of LICS 1996, pp. 278–292. IEEE Computer Society Press (1996)

    Google Scholar 

  24. Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94–124 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  25. HyCreate: a tool for overapproximating reachability of hybrid automata. http://stanleybak.com/projects/hycreate/hycreate.html

  26. Kong, S., Gao, S., Chen, W., Clarke, E.: dReach: \(\delta \)-reachability analysis for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 200–205. Springer, Heidelberg (2015)

    Google Scholar 

  27. Le Guernic, C.: Reachability analysis of hybrid systems with linear continuous dynamics. Ph.D. thesis, Université Joseph-Fourier-Grenoble I, France (2009)

    Google Scholar 

  28. Le Guernic, C., Girard, A.: Reachability analysis of linear systems using support functions. Nonlinear Anal. Hybrid Syst. 4(2), 250–262 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Lygeros, J.: Lecture notes on hybrid systems. In: Notes for the ENSIETA 2004 Workshop (2004)

    Google Scholar 

  30. Maka, H., Frehse, G., Krogh, B.H.: Polyhedral domains and widening for verification of numerical programs. In: NSV-II: Second International Workshop on Numerical Software Verification (2009)

    Google Scholar 

  31. Nedialkov, N.S.: VNODE-LP - A validated solver for initial value problems in ordinary differential equations. Technical Report CAS-06-06-NN, Department of Computing and Software, McMaster University, Ontario (2006)

    Google Scholar 

  32. Platzer, A., Quesel, J.-D.: KeYmaera: a hybrid theorem prover for hybrid systems (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 171–178. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  33. Platzer, A.: Differential dynamic logic for hybrid systems. J. Autom. Reason. 41(2), 143–189 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  34. ProHVer: Safety verification for probabilistic hybrid systems. http://depend.cs.uni-sb.de/tools/prohver/

  35. Ramdani, N., Meslem, N., Candau, Y.: A hybrid bounding method for computing an over-approximation for the reachable set of uncertain nonlinear systems. IEEE Trans. Autom. Control 54(10), 2352–2364 (2009)

    Article  MathSciNet  Google Scholar 

  36. Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 573–589. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  37. Shao, Z., Liu, J.: Spatio-temporal hybrid automata for cyber-physical systems. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) ICTAC 2013. LNCS, vol. 8049, pp. 337–354. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  38. Sproston, J.: Decidable model checking of probabilistic hybrid automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, p. 31. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Stefan Schupp, Erika Ábrahám, Xin Chen, Ibtissem Ben Makhlouf & Stefan Kowalewski

  2. Verimag, Gières, France

    Goran Frehse

  3. University of Colorado, Boulder, CO, USA

    Sriram Sankaranarayanan

Authors
  1. Stefan Schupp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erika Ábrahám
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ibtissem Ben Makhlouf
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Goran Frehse
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sriram Sankaranarayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Stefan Kowalewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Schupp .

Editor information

Editors and Affiliations

  1. Halmstad University, Halmstad, Sweden

    Mohammad Reza Mousavi

  2. University of Gothenburg, Gothenburg, Sweden

    Christian Berger

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Schupp, S. et al. (2015). Current Challenges in the Verification of Hybrid Systems. In: Mousavi, M., Berger, C. (eds) Cyber Physical Systems. Design, Modeling, and Evaluation. CyPhy 2015. Lecture Notes in Computer Science(), vol 9361. Springer, Cham. https://doi.org/10.1007/978-3-319-25141-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25141-7_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25140-0

  • Online ISBN: 978-3-319-25141-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation