Skip to main content

Modeling the Supervisory Control Theory with Alloy

  • Conference paper
Abstract State Machines, Alloy, B, VDM, and Z (ABZ 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7316))

  • 860 Accesses

Abstract

Scientific literature reveals that symbolic representation techniques behind some formal methods are attractive to synthesize parts or verify properties of large discrete event systems. They involve, however, complex encoding schemata and fine tuning heuristic parameters in order to translate specific problems into efficient BDD or SAT-based representations. This approach may be too costly when the main goal is to explore a theory, understand by simulation its underlying concepts and computation procedures, and conduct experiments by applying them to small problems. Based on previous work with Alloy on the synthesis of observers and nonblocking supervisors of a system organized hierarchically with a flat state space estimated to 1031 states, this paper investigates more deeply issues raised with its use in the modeling and prototyping of the supervisory control theory, including the application of models to practical problems. This study was conducted in a broader context than just hierarchical control since it embraces various variants of this theory.

The research described in this paper was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barbeau, M., Custeau, G., St-Denis, R.: An algorithm for computing the mask value of the supremal normal sublanguage of a legal language. IEEE Trans. Automat. Contr. 40, 699–703 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beyer, D., Noack, A., Lewerentz, C.: Efficient relational calculation for software analysis. IEEE Trans. Soft. Eng. 31, 137–149 (2005)

    Article  Google Scholar 

  3. Chakib, H., Khoumsi, A.: Multi-decision supervisory control: parallel decentralized architectures cooperating for controlling discrete event systems. IEEE Trans. Automat. Contr. 56, 2608–2622 (2011)

    Article  MathSciNet  Google Scholar 

  4. Claessen, K., Een, N., Sheeran, M., Sórensson, N., Voronov, A., Åkesson, K.: SAT-solving in practice, with a tutorial example from supervisory control. J. Discrete Event Dynamic Systems: Theory and Appl. 19, 495–524 (2009)

    Article  MATH  Google Scholar 

  5. Côté, D., Fraikin, B., Frappier, M., St-Denis, R.: A SAT-Based Approach for the Construction of Reusable Control System Components. In: Salaün, G., Schätz, B. (eds.) FMICS 2011. LNCS, vol. 6959, pp. 52–67. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Fernandez, J.-C.: An implementation of an efficient algorithm for bisimulation equivalence. Sci. Comput. Program. 13, 219–236 (1990)

    Article  MATH  Google Scholar 

  7. Hill, R.C., Cury, J.E.R., de Queiroz, M.H., Tilbury, D.M., Lafortune, S.: Multi-level hierarchical interface-based supervisory control. Automatica 46, 1152–1164 (2010)

    Article  MATH  Google Scholar 

  8. Jackson, D.: Software Abstractions. MIT Press, Cambridge (2006)

    Google Scholar 

  9. Kumar, R., Garg, V.K.: Modeling and Control of Logical Discrete Event Systems. Kluwer Academic Publishers, Boston (1995)

    Book  MATH  Google Scholar 

  10. Kumar, R., Takai, S.: Inference-based ambiguity management in decentralized decision-making: decentralized control of discrete event systems. IEEE Trans. Automat. Contr. 52, 1783–1794 (2007)

    Article  MathSciNet  Google Scholar 

  11. Li, Y.: Control of vector discrete-event systems. Ph.D. Thesis, Graduate Dept. of Electrical and Computer Engineering, University of Toronto, Toronto, Canada (1991)

    Google Scholar 

  12. Ma, C., Wonham, W.M.: Nonblocking Supervisory Control of State Tree Structures. LNCIS, vol. 317. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  13. Milner, R.: Communication and Concurrency. Prentice Hall, New York (1989)

    Google Scholar 

  14. Ramadge, P.J., Wonham, W.M.: The control of discrete event systems. Proc. of the IEEE 77, 81–98 (1989)

    Article  Google Scholar 

  15. Su, R., van Schuppen, J.H., Rooda, J.E.: Aggregative synthesis of distributed supervisors based on automaton abstraction. IEEE Trans. Automat. Contr. 55, 1627–1640 (2010)

    Article  Google Scholar 

  16. Torlak, E., Jackson, D.: Kodkod: A Relational Model Finder. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 632–647. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Wong, K.C., Wonham, W.M.: Hierarchical control of discrete-event systems. J. Discrete Event Dynamic Systems: Theory and Appl. 6, 241–273 (1996)

    Article  MATH  Google Scholar 

  18. Wong, K.C., Wonham, W.M.: On the computation of observers in discrete-event systems. J. Discrete Event Dynamic Systems: Theory and Appl. 14, 55–107 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wonham, W.M., Ramadge, P.J.: On the supremal controllable sublanguage of a given language. SIAM J. Control and Optimization 25, 637–659 (1987)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fraikin, B., Frappier, M., St-Denis, R. (2012). Modeling the Supervisory Control Theory with Alloy . In: Derrick, J., et al. Abstract State Machines, Alloy, B, VDM, and Z. ABZ 2012. Lecture Notes in Computer Science, vol 7316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30885-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30885-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30884-0

  • Online ISBN: 978-3-642-30885-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics