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Supervisory Control of Extended Timed Event Graphs

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Abstract

This paper describes the dynamic behavior of extended timed event graphs related to place delay in the dioid framework. By Cofer and Garg's supervisory control theory|3|, we address control problems of extended timed events graphs. Supervisory control of extended timed event graphs (a class of discrete event dynamic systems) is studied in the dioid framework, a necessary and sufficient condition for the ideals of the set of firing time sequences of transitions to be controllable is presented. We prove all the strongly controllable subsets can form a complete lattice.

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References

  1. Baccelli, F.L., Cohen, G., Olsder, G.J., Quadrat, J.P. Synchronization and linearity—an algebra for discrete event systems. Wiley, New York, 1992

  2. Chen, W.D., Qi, X.D. The discrete event dynamic system—max algebra methods. Science Press, Beijing, 1994

  3. Cofer, D.D., Garg, V.K. Supervisory control of real-time discrete event systems using lattice theory. IEEE Trans. Automat. Control, 41:199–209 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cohen, G., Moller, P., Quadrat, J.P., Viot, M. Algebraic tools for the performance evaluation of discrete event systems. Proc. IEEE. 77:39–58 (1989)

    Article  Google Scholar 

  5. Cuninghame-Green, R.A. Min-max algebra. Springer, Berlin, 1979

  6. Dai, H.P. Studies on theory and application of computer integrated process systems. Ph.D dissertation, institute of industrial process control, Zhejiang university, 1998

  7. Kumar, R., Garg, V.K. Extremal solutions of inequations over lattices with applications to supervisory control. In proceedings of the 33nd conference on Decision and Control. Lake Buena Vista, 3636–3641, 1994

  8. Kuntzmann, J. Theorie des reseaux graphes. Dunod, Paris, 1972

  9. Ramadge, P.J, Wonham, W.M. Supervisory control of a class of discrete event processes. SIAM J. Control. Optim., 25:206–230 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Takai, S. A characterization of realizable behavior in supervisory control of timed event graphs. Automatica, 33(11):2077–2080 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Takai, S., Kodama, S. Formulae for the extremal contrallable sequences in timed event graphs. IEEE Trans. Automat. Control, 43(10):1465–1468 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Zhi-bing Zhuo & Wen-de Chen

Authors
  1. Zhi-bing Zhuo
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  2. Wen-de Chen
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Correspondence to Zhi-bing Zhuo.

Additional information

Supported by National Key Project of China and the National Sciences Foundation of China (Grant No. 69874040).

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Zhuo, Zb., Chen, Wd. Supervisory Control of Extended Timed Event Graphs. Acta Mathematicae Applicatae Sinica, English Series 19, 281–288 (2003). https://doi.org/10.1007/s10255-003-0103-5

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  • DOI: https://doi.org/10.1007/s10255-003-0103-5

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