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A CEGAR Tool for the Reachability Analysis of PLC-Controlled Plants Using Hybrid Automata

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Formalisms for Reuse and Systems Integration (FMI 2014)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 346))

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Abstract

In this paper we address the safety analysis of chemical plants controlled by programmable logic controllers (PLCs). We consider sequential function charts (SFCs) for the programming of the PLCs, extended with the specification of the dynamic plant behavior. The resulting hybrid SFC models can be transformed to hybrid automata, opening the way to the application of advanced techniques for their reachability analysis. However, the hybrid automata models are often too large to be analyzed. To keep the size of the models moderate, we propose a counterexample-guided abstraction refinement (CEGAR) approach, which starts with the purely discrete SFC model of the controller and extends it with those parts of the dynamic behavior, which are relevant for proving or disproving safety. Our algorithm can deal with urgent locations and transitions, and non-convex invariants. We integrated the CEGAR approach in the analysis tool spaceex and present an example.

This work was partly supported by the German Research Foundation (DFG) as part of the Research Training Group “AlgoSyn” (GRK 1298) and the DFG research project “HyPro” (AB 461/4-1).

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References

  1. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138, 3–34 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Dang, T., Ivančić, F.: Counter-example guided predicate abstraction of hybrid systems. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 208–223. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Asarin, E., Dang, T., Maler, O.: The d/dt tool for verification of hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 365–770. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. Balluchi, A., Casagrande, A., Collins, P., Ferrari, A., Villa, T., Sangiovanni-Vincentelli, A.L.: Ariadne: A framework for reachability analysis of hybrid automata. In: Proc. of MTNS 2006 (2006)

    Google Scholar 

  5. Baresi, L., Carmeli, S., Monti, A., Pezzè, M.: PLC programming languages: A formal approach. In: Proc. of Automation 1998. ANIPLA (1998)

    Google Scholar 

  6. Bauer, N.: Formale Analyse von Sequential Function Charts. Ph.D. thesis, Universität Dortmund (2004)

    Google Scholar 

  7. Bauer, N., Huuck, R., Lukoschus, B., Engell, S.: A unifying semantics for sequential function charts. In: Ehrig, H., Damm, W., Desel, J., Große-Rhode, M., Reif, W., Schnieder, E., Westkämper, E. (eds.) INT 2004. LNCS, vol. 3147, pp. 400–418. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Bogomolov, S., Donzé, A., Frehse, G., Grosu, R., Johnson, T.T., Ladan, H., Podelski, A., Wehrle, M.: Abstraction-based guided search for hybrid systems. In: Bartocci, E., Ramakrishnan, C.R. (eds.) SPIN 2013. LNCS, vol. 7976, pp. 117–134. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  9. 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 

  10. Clarke, E., Fehnker, A., Han, Z., Krogh, B.: Abstraction and counterexample-guided refinement in model checking of hybrid systems. Int. Journal of Foundations of Computer Science 14(04), 583–604 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Clarke, E., Fehnker, A., Han, Z., Krogh, B., Stursberg, O., Theobald, M.: Verification of hybrid systems based on counterexample-guided abstraction refinement. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 192–207. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)

    Google Scholar 

  13. Dierks, H., Kupferschmid, S., Larsen, K.: Automatic abstraction refinement for timed automata. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 114–129. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Engell, S., Lohmann, S., Stursberg, O.: Verification of embedded supervisory controllers considering hybrid plant dynamics. Int. Journal of Software Engineering and Knowledge Engineering 15(2), 307–312 (2005)

    Article  Google Scholar 

  15. Fehnker, A., Clarke, E., Jha, S., Krogh, B.: Refining abstractions of hybrid systems using counterexample fragments. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 242–257. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. 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 

  17. Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. Int. Journal on Software Tools for Technology Transfer 10, 263–279 (2008)

    Article  MathSciNet  Google Scholar 

  18. Frey, G., Litz, L.: Formal methods in PLC programming. In: Proc. of SMC 2000, vol. 4, pp. 2431–2436. IEEEXplore (2000)

    Google Scholar 

  19. Girard, A., Pappas, G.J.: Approximation metrics for discrete and continuous systems. TAC 2007 52(5), 782–798 (2007)

    Google Scholar 

  20. Hassapis, G., Kotini, I., Doulgeri, Z.: Validation of a SFC software specification by using hybrid automata. In: Proc. of INCOM 1998, pp. 65–70. Pergamon (1998)

    Google Scholar 

  21. Henzinger, T.A., Ho, P., Wong-Toi, H.: Hytech: A model checker for hybrid systems. Int. Journal on Software Tools for Technology Transfer 1(1-2), 110–122 (1997)

    Article  MATH  Google Scholar 

  22. Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Computer and System Sciences 57(1), 94–124 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  23. Herceg, M., Kvasnica, M., Jones, C.N., Morari, M.: Multi-Parametric Toolbox 3.0. In: Proc. of the ECC 2013, Zürich, Switzerland, pp. 502–510 (2013)

    Google Scholar 

  24. Int. Electrotechnical Commission: Programmable Controllers, Part 3: Programming Languages, 61131–61133 (2003)

    Google Scholar 

  25. Jha, S.K., Krogh, B.H., Weimer, J.E., Clarke, E.M.: Reachability for linear hybrid automata using iterative relaxation abstraction. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 287–300. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  26. Kurzhanskiy, A., Varaiya, P.: Ellipsoidal toolbox. Tech. rep., EECS, UC Berkeley (2006)

    Google Scholar 

  27. Lukoschus, B.: Compositional Verification of Industrial Control Systems - Methods and Case Studies. Ph.D. thesis, Christian-Albrechts-Universität zu Kiel (2005)

    Google Scholar 

  28. Minopoli, S., Frehse, G.: Non-convex invariants and urgency conditions on linear hybrid automata. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 176–190. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  29. Mitchell, I., Tomlin, C.: Level set methods for computation in hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 310–323. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  30. Nellen, J., Ábrahám, E.: Hybrid sequential function charts. In: Proc. of MBMV 2012, pp. 109–120. Verlag Dr. Kovac (2012)

    Google Scholar 

  31. Nellen, J., Ábrahám, E.: A CEGAR approach for the reachability analysis of PLC-controlled chemical plants. In: Proc. of FMi 2014 (2014)

    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. Prabhakar, P., Duggirala, P.S., Mitra, S., Viswanathan, M.: Hybrid automata-based CEGAR for rectangular hybrid systems. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 48–67. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  34. Segelken, M.: Abstraction and counterexample-guided construction of ω-automata for model checking of step-discrete linear hybrid models. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 433–448. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Johanna Nellen, Erika Ábrahám & Benedikt Wolters

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  1. Johanna Nellen
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  2. Erika Ábrahám
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  3. Benedikt Wolters
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Correspondence to Johanna Nellen .

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Editors and Affiliations

  1. Ecole Nationale Supérieure d'Informatique, Alger, Algeria

    Thouraya Bouabana-Tebibel

  2. SPAWAR Systems Center Pacific, San Diego, California, USA

    Stuart H. Rubin

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Nellen, J., Ábrahám, E., Wolters, B. (2015). A CEGAR Tool for the Reachability Analysis of PLC-Controlled Plants Using Hybrid Automata. In: Bouabana-Tebibel, T., Rubin, S. (eds) Formalisms for Reuse and Systems Integration. FMI 2014. Advances in Intelligent Systems and Computing, vol 346. Springer, Cham. https://doi.org/10.1007/978-3-319-16577-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-16577-6_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16576-9

  • Online ISBN: 978-3-319-16577-6

  • eBook Packages: EngineeringEngineering (R0)

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