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Current Challenges in the Verification of Hybrid Systems

  • Stefan SchuppEmail author
  • Erika Ábrahám
  • Xin Chen
  • Ibtissem Ben Makhlouf
  • Goran Frehse
  • Sriram Sankaranarayanan
  • Stefan Kowalewski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Hybrid systems Verification Reachability analysis Tool support Benchmarks 

References

  1. 1.
    Althoff, M., Dolan, J.M.: Online verification of automated road vehicles using reachability analysis. IEEE Trans. Robot. 30(4), 903–918 (2014)CrossRefGoogle Scholar
  2. 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. 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. 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. 5.
    Barrett, C., Stump, A., Tinelli, C.: The satisfiability modulo theories library (SMT-LIB) (2010). http://www.SMT-LIB.org
  6. 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) CrossRefGoogle Scholar
  7. 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. 8.
  9. 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)CrossRefGoogle Scholar
  10. 10.
    Chen, X.: Reachability Analysis of Non-Linear Hybrid Systems Using Taylor Models. Ph.D. thesis, RWTH Aachen University, Germany (2015)Google Scholar
  11. 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. 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) CrossRefGoogle Scholar
  13. 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. 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. 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. 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. 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. 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. 19.
    Frehse, G.: Reachability of hybrid systems in space-time. In: Proceedings of EMSOFT 2015. ACM (2015)Google Scholar
  20. 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) CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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) CrossRefGoogle Scholar
  23. 23.
    Henzinger, T.: The theory of hybrid automata. In: Proceedings of LICS 1996, pp. 278–292. IEEE Computer Society Press (1996)Google Scholar
  24. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    HyCreate: a tool for overapproximating reachability of hybrid automata. http://stanleybak.com/projects/hycreate/hycreate.html
  26. 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. 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. 28.
    Le Guernic, C., Girard, A.: Reachability analysis of linear systems using support functions. Nonlinear Anal. Hybrid Syst. 4(2), 250–262 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Lygeros, J.: Lecture notes on hybrid systems. In: Notes for the ENSIETA 2004 Workshop (2004)Google Scholar
  30. 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. 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. 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) CrossRefGoogle Scholar
  33. 33.
    Platzer, A.: Differential dynamic logic for hybrid systems. J. Autom. Reason. 41(2), 143–189 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    ProHVer: Safety verification for probabilistic hybrid systems. http://depend.cs.uni-sb.de/tools/prohver/
  35. 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)MathSciNetCrossRefGoogle Scholar
  36. 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) CrossRefGoogle Scholar
  37. 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) CrossRefGoogle Scholar
  38. 38.
    Sproston, J.: Decidable model checking of probabilistic hybrid automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, p. 31. Springer, Heidelberg (2000) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Stefan Schupp
    • 1
    Email author
  • Erika Ábrahám
    • 1
  • Xin Chen
    • 1
  • Ibtissem Ben Makhlouf
    • 1
  • Goran Frehse
    • 2
  • Sriram Sankaranarayanan
    • 3
  • Stefan Kowalewski
    • 1
  1. 1.RWTH Aachen UniversityAachenGermany
  2. 2.VerimagGièresFrance
  3. 3.University of ColoradoBoulderUSA

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