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Supervisory Control

  • Christos G. Cassandras
  • Stéphane Lafortune
Part of the The Kluwer International Series on Discrete Event Dynamic Systems book series (DEDS, volume 11)

Abstract

The situation under consideration in this chapter is that of a given DES, modeled at the untimed (or logical) level of abstraction, and whose behavior must be modified by feedback control in order to achieve a given set of specifications. This is reminiscent of the feedback control loop introduced in Chapter 1, in Section 1.2.8. Let us assume that the given DES is modeled by automaton G, where the state space of G need not be finite. Let E be the event set of G. Automaton G models the “uncontrolled behavior” of the DES. The premise is that this behavior is not satisfactory and must be “modified” by control; modifying the behavior is to be understood as restricting the behavior to a subset of £(G). In order to alter the behavior of G we introduce a supervisor, supervisors will be denoted by S. Note that we separate the “plant” G from the “controller” (or supervisor) S, as is customary in control theory. This raises two questions: (a) What do we mean by specifications? and (b) How does S modify the behavior of G?

Keywords

Controllable Event Regular Language Supervisory Control Unobservable Event Uncontrollable Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Selected References

Book or survey papers on supervisory control

  1. Kumar, R., and V.K. Garg, Modeling and Control of Logical Discrete Event Systems, Kluwer Academic Publishers, Boston, 1995.CrossRefMATHGoogle Scholar
  2. Ramadge, P.J., and W.M. Wonham, “The control of discrete event systems,” Proceedings of the IEEE, Vol. 77, No. 1, pp. 81–98, January 1989.CrossRefGoogle Scholar
  3. Thistle, J.G., “Supervisory control of discrete event systems,” Mathematical and Computer Modelling, Vol. 23, No. 11 /12, pp. 25–53, 1996.MathSciNetCrossRefMATHGoogle Scholar

Original references on main concepts presented in this chapter

  1. Chen, E., and S. Lafortune. “Dealing with blocking in supervisory control of discrete event systems,” IEEE Transactions on Automatic Control, Vol. 36, No. 6, pp. 724–735, June 1991.MathSciNetCrossRefGoogle Scholar
  2. Cieslak, R., C. Desclaux, A. Fawaz, and P. Varaiya, “Supervisory control of discrete-event processes with partial observations,” IEEE Transactions on Automatic Control, Vol. 33, No. 3, pp. 249–260, March 1988.CrossRefMATHGoogle Scholar
  3. Lafortune, S., and E. Chen, “The infimal closed controllable super-language and its application in supervisory control,” IEEE Transactions on Automatic Control, Vol. 35, No. 4, pp. 398–405, April 1990.MathSciNetCrossRefMATHGoogle Scholar
  4. Lin, F., and W.M. Wonham, “On observability of discrete-event systems,” Information Sciences, Vol. 44, pp. 173–198, 1988.MathSciNetCrossRefMATHGoogle Scholar
  5. Ramadge, P.J., and W.M. Wonham, “Supervisory control of a class of discrete event processes,” SIAM Journal on Control and Optimization, Vol. 25, No. 1, pp. 206–230, January 1987.MathSciNetCrossRefMATHGoogle Scholar
  6. Rudie, K., and W. M. Wonham, “Think globally, act locally: Decentralized supervisory control,” IEEE Transactions on Automatic Control, Vol. 37, No. 11, pp. 1692–1708, November 1992.MathSciNetCrossRefMATHGoogle Scholar
  7. Wonham, W.M., and P.J Ramadge, “On the supremal controllable sublanguage of a given language,” SIAM Journal on Control and Optimization, Vol. 25, No. 3, pp. 637–659, May 1987.MathSciNetCrossRefGoogle Scholar
  8. Wonham, W.M., and P.J. Ramadge, “Modular supervisory control of discrete-event systems,” Mathematics of Control, Signals, and Systems, Vol. 1, No. 1, pp. 13–30, 1988.MathSciNetCrossRefMATHGoogle Scholar

For further reading on some topics only briefly covered in this chapter

  1. Ben Hadj-Alouane, N., S. Lafortune, and F. Lin, “Centralized and distributed algorithms for on-line synthesis of maximal control policies under partial observation,” Discrete Event Dynamic Systems: Theory and Applications, Vol. 6, No. 4, pp. 379–427, October 1996.CrossRefMATHGoogle Scholar
  2. Brandt, R. D., V. Garg, R. Kumar, F. Lin, S. I. Marcus, and W. M. Wonham, “Formulas for calculating supremal controllable and normal sublanguages,” Systems & Control Letters, Vo. 15, No. 2, pp. 111117, August 1990.Google Scholar
  3. Cho, H., and S.I. Marcus, “On supremal languages of classes of sub-languages that arise in supervisor synthesis problems with partial observation,” Mathematics of Control, Signals, and Systems, Vol. 2, No. 2, pp. 47–69, 1989.MathSciNetCrossRefMATHGoogle Scholar
  4. Inan, K., “An algebraic approach to supervisory control,” Mathematics of Control, Signals, and Systems, Vol. 5, pp. 151–164, 1992.MathSciNetCrossRefMATHGoogle Scholar
  5. Kumar, R., and M. Shayman, “Formulas relating controllability, observability, and co-observability,” Automatica, Vol. 34, No. 2, pp. 211–215, 1998.MathSciNetCrossRefMATHGoogle Scholar
  6. Lafortune, S., and F. Lin, “On tolerable and desirable behaviors in supervisory control of discrete event systems,” Discrete Event Dynamic Systems: Theory and Applications, Vol. 1, No. 1, pp. 61–92, May 1991.CrossRefMATHGoogle Scholar
  7. Lin, F., A. Vaz, and W.M. Wonham, “Supervisor specification and synthesis for discrete event systems,” International Journal of Control, Vol. 48, No. 1, pp. 321–332, 1988.MathSciNetCrossRefMATHGoogle Scholar
  8. Rudie, K., and J.C. Willems, “The computational complexity of decentralized discrete-event control problems,” IEEE Transactions on Automatic Control, Vol. 40, No. 7, pp. 1313–1319, July 1995.MathSciNetCrossRefMATHGoogle Scholar
  9. Rudie, K., and W.M. Wonham, “The infimal prefix-closed and observable superlanguage of a given language,” Systems & Control Letters, Vol. 15, pp. 361–371, 1990.MathSciNetCrossRefMATHGoogle Scholar
  10. Tsitsiklis, J.N., “On the control of discrete-event dynamical systems,” Mathematics of Control, Signals, and Systems, Vol. 2, No. 1, pp. 95–107, 1989.MathSciNetCrossRefMATHGoogle Scholar
  11. Vaz, A., and W.M. Wonham, “On supervisor reduction in discrete-event systems,” International Journal of Control, Vol. 44, No. 2, pp. 475–491, 1986.MathSciNetCrossRefMATHGoogle Scholar

Some applications of supervisory control

  1. Balemi, S., G. J. Hoffmann, P. Gyugyi, H. Wong-Toi, and G. F. Franklin, “Supervisory control of a rapid thermal multiprocessor,” IEEE Transactions on Automatic Control, Vol. 38, No. 7, pp. 1040–1059, July 1993.Google Scholar
  2. Brandin, B.A., “The Real-Time Supervisory Control of an Experimental Manufacturing Cell,” IEEE Transactions on Robotics and Automation, Vol. 12, No. 1, pp. 1–14, February 1996.CrossRefGoogle Scholar
  3. Lafortune, S., “Modeling and analysis of transaction execution in database systems,” IEEE Transactions on Automatic Control, Vol. 33, No. 5, pp. 439–447, May 1988.CrossRefGoogle Scholar
  4. Rudie, K., W.M. Wonham, “Supervisory control of communicating processes,” in Protocol Specification, Testing, and Verification X, L. Logrippo, R. L. Probert, and H. Ural (Eds.), Elsevier Science Publishers, 1990, pp. 243–257.Google Scholar
  5. Thistle, J.G., R.P. Malhamé, H.-H. Hoang, and S. Lafortune, “Feature interaction modelling, detection and resolution: A supervisory control approach,” in Feature Interactions in Telecommunication Networks IV, P. Dini, R. Boutaba, and L. Logrippo, Eds., IOS Press, 1997, pp. 93–107.Google Scholar

Other paradigms for control of untimed DES

  1. Caines, P.E., and S. Wang,“ ”COCOLOG: A conditional observer and controller logic for finite machines,“ SIAM Journal on Control and Optimization, Vol. 33, No. 6, pp. 1687–1715, November 1995.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Christos G. Cassandras
    • 1
  • Stéphane Lafortune
    • 2
  1. 1.Boston UniversityUSA
  2. 2.The University of MichiganUSA

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