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A Supervisory Control Algorithm Based on Property-Directed Reachability

  • Koen Claessen
  • Jonatan KilhamnEmail author
  • Laura Kovács
  • Bengt Lennartson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10629)

Abstract

We present an algorithm for synthesising a controller (supervisor) for a discrete event system (DES) based on the property-directed reachability (PDR) model checking algorithm. The discrete event systems framework is useful in both software, automation and manufacturing, as problems from those domains can be modelled as discrete supervisory control problems. As a formal framework, DES is also similar to domains for which the field of formal methods for computer science has developed techniques and tools. In this paper, we attempt to marry the two by adapting PDR to the problem of controller synthesis. The resulting algorithm takes as input a transition system with forbidden states and uncontrollable transitions, and synthesises a safe and minimally-restrictive controller, correct-by-design. We also present an implementation along with experimental results, showing that the algorithm has potential as a part of the solution to the greater effort of formal supervisory controller synthesis and verification.

Keywords

Supervisory control Discrete-event systems Property-directed reachability Synthesis Verification Symbolic transition system 

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References

  1. 1.
    Biere, A.: AIGER (2014). http://fmv.jku.at/aiger/ (visited on July 24, 2017)
  2. 2.
    Bradley, A.R.: SAT-Based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-18275-4_7 CrossRefGoogle Scholar
  3. 3.
    Cimatti, A., Griggio, A.: Software model checking via IC3. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 277–293. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31424-7_23 CrossRefGoogle Scholar
  4. 4.
    Eén, N., Mishchenko, A., Brayton, R.: Efficient implementation of property directed reachability. In: Proceedings of the International Conference on Formal Methods in Computer-Aided Design, FMCAD 2011, pp. 125–134. FMCAD Inc., Austin, Texas (2011). http://dl.acm.org/citation.cfm?id=2157654.2157675. ISBN: 978-0-9835678-1-3
  5. 5.
    Eén, N., Sörensson, N.: Temporal Induction by Incremental SAT Solving. Electronic Notes in Theoretical Computer Science 89(4), 543–560 (2003). DOI: http://dx.doi.org/10.1016/S1571-0661(05)82542-3. ISSN: 1571–0661
  6. 6.
    Fei, Z., et al.: A symbolic approach to large-scale discrete event systems modeled as finite automata with variables. In: 2012 IEEE International Conference on Automation Science and Engineering (CASE), pp. 502–507, August 2012. DOI:  https://doi.org/10.1109/CoASE.2012.6386479
  7. 7.
    Hassan, Z., Bradley, A.R., Somenzi, F.: Incremental, inductive CTL model checking. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 532–547. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31424-7_38 CrossRefGoogle Scholar
  8. 8.
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall Inc., Upper Saddle River, NJ, USA (1985). ISBN: 0-13-153271-5Google Scholar
  9. 9.
    Hoder, K., Bjørner, N.: Generalized Property Directed Reachability. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 157–171. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31612-8_13 CrossRefGoogle Scholar
  10. 10.
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 3rd edn. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA (2006). ISBN: 0321462254Google Scholar
  11. 11.
    Kumar, R., Garg, V., Marcus, S.I.: Predicates and predicate transformers for supervisory control of discrete event dynamical systems. IEEE Transactions on Automatic Control 38(2) , pp. 232–247 (1993). DOI:  https://doi.org/10.1109/9.250512. ISSN: 0018–9286
  12. 12.
    Leduc, R.J., Lawford, M., Wonham, W.M.: Hierarchical interface-based supervisory control-part II: parallel case. IEEE Transactions on Automatic Control 50(9), 1336–1348 (2005). DOI:  https://doi.org/10.1109/TAC.2005.854612. ISSN, pp. 0018–9286
  13. 13.
    Malik, R.: Waters/Supremica IDE. http://www.cs.waikato.ac.nz/.robi/download/_waters/ (visited on July 24, 2017)
  14. 14.
    Miremadi, S., Lennartson, B., Akesson, K.: A BDD-Based Approach for Modeling Plant and Supervisor by Extended Finite Automata. IEEE Transactions on Control Systems Technology 20(6), 1421–1435 (2012). DOI:  https://doi.org/10.1109/TCST.2011.2167150. ISSN: 1063–6536
  15. 15.
    Miremadi, S., Akesson, K., et al.: Solving two supervisory control benchmark problems using Supremica. In: 2008 9th International Workshop on Discrete Event Systems, pp. 131–136, May 2008. DOI: https://doi.org/10.1109/WODES.2008.4605934
  16. 16.
    Ramadge, P.J., Wonham, W.M.: The control of discrete event systems. Proceedings of the IEEE, Special Issue on Discrete Event Dynamic Systems 77(1), 81–98 (1989). ISSN: 0018–9219Google Scholar
  17. 17.
    Shoaei, M.R.: Incremental and Hierarchical Deadlock-Free Control of Discrete Event Systems with Variables: A Symbolic and Inductive Approach. PhD thesis, Series 3827. Chalmers University of Technology, Dept. of Signals and Systems, Automation, pp. 44–45 (2015). ISBN: 978-91-7597-146-9Google Scholar
  18. 18.
    Shoaei, M.R., Kovács, L., Lennartson, B.: Supervisory control of discrete-event systems via IC3. In: Yahav, E. (ed.) HVC 2014. LNCS, vol. 8855, pp. 252–266. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-13338-6_19 Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Koen Claessen
    • 1
  • Jonatan Kilhamn
    • 1
    Email author
  • Laura Kovács
    • 1
    • 3
  • Bengt Lennartson
    • 2
  1. 1.Department of Computer Science and EngineeringChalmers University of TechnologyGothenburgSweden
  2. 2.Department of Electrical EngineeringChalmers University of TechnologyGöthenburgSweden
  3. 3.Faculty of InformaticsVienna University of TechnologyViennaAustria

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