Predictability and control synthesis

Philippe Declerck

Kybernetika (1999)

  • Volume: 35, Issue: 1, page [25]-38
  • ISSN: 0023-5954

Abstract

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Processes modeled by a timed event graph may be represented by a linear model in dioïd algebra. The aim of this paper is to make temporal control synthesis when state vector is unknown. This information loss is compensated by the use of a simple model, the “ARMA” equations, which enables to introduce the concept of predictability. The comparison of the predictable output trajectory with the desired output determines the reachability of the objective.

How to cite

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Declerck, Philippe. "Predictability and control synthesis." Kybernetika 35.1 (1999): [25]-38. <http://eudml.org/doc/33407>.

@article{Declerck1999,
abstract = {Processes modeled by a timed event graph may be represented by a linear model in dioïd algebra. The aim of this paper is to make temporal control synthesis when state vector is unknown. This information loss is compensated by the use of a simple model, the “ARMA” equations, which enables to introduce the concept of predictability. The comparison of the predictable output trajectory with the desired output determines the reachability of the objective.},
author = {Declerck, Philippe},
journal = {Kybernetika},
keywords = {synthesis problems; predictability; ARMA model; Dioid algebra; reachability of the objective; synthesis problems; predictability; ARMA model; Dioid algebra; reachability of the objective},
language = {eng},
number = {1},
pages = {[25]-38},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Predictability and control synthesis},
url = {http://eudml.org/doc/33407},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Declerck, Philippe
TI - Predictability and control synthesis
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 1
SP - [25]
EP - 38
AB - Processes modeled by a timed event graph may be represented by a linear model in dioïd algebra. The aim of this paper is to make temporal control synthesis when state vector is unknown. This information loss is compensated by the use of a simple model, the “ARMA” equations, which enables to introduce the concept of predictability. The comparison of the predictable output trajectory with the desired output determines the reachability of the objective.
LA - eng
KW - synthesis problems; predictability; ARMA model; Dioid algebra; reachability of the objective; synthesis problems; predictability; ARMA model; Dioid algebra; reachability of the objective
UR - http://eudml.org/doc/33407
ER -

References

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  1. Baccelli F., Cohen G., Olsder G. J., Quadrat J. P., Synchronization and Linearity, An Algebra for Discrete Event Systems. Wiley, New York 1992 Zbl0824.93003MR1204266
  2. Bracker H., Algorithms and Applications in Timed Discrete Event Systems, Ph.D thesis, Delft University of Technology, 1993 
  3. Brat G. P., Garg V. K., A max–plus algebra of signals for the supervisory control of real–time discrete event systems, In: 9th Symposium of the IFAC on Information Control in Manufacturing, Nancy–Metz 1998 
  4. Cofer D. D., Garg V. K., A timed model for the control of discrete event systems involving decisions in the max/plus algebra, In: Proc. 31st Conference on Decision and Control, Tucson 1992 
  5. Cofer D. D., Control and Analysis of Real–Time Discrete Event Systems, Ph.D. Thesis, University of Texas, Austin 1995 
  6. Cofer D. D., Garg V. K., 10.1109/9.481519, IEEE Trans. Automat. Control 41 (1996), 2, 199–209 (1996) Zbl0846.93005MR1375752DOI10.1109/9.481519
  7. Cohen G., Gaubert S., Quadrat J.-P., From first to second–order theory of linear discrete event systems, In: 1st IFAC World Congress, Sydney 1993 
  8. Declerck, Ph., “ARMA” model and admissible trajectories in timed event graphs, In: CESA’96, IMACS, IEEE–SMC, Lille 1996 
  9. Declerck, Ph., Control synthesis using the state equations and the “ARMA” model in timed event graphs, In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997 
  10. Declerck, Ph., Mares M., Temporal control synthesis and failure recovery, In: 9th Symposium of the IFAC on Information Control in Manufacturing, Nancy–Metz 1998 
  11. Gaubert S., Théorie des systèmes linéaires dans les dioïdes, Ph.D Thesis, Ecole des Mines de Paris 1992 
  12. Gazarik M. J., Kamen E. W., Reachability and observability of linear systems over max–plus, In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997, revised version: Kybernetika 35 (1999), 2–12 (1997) MR1705526
  13. Gondran M., Minoux M., Graphes et algorithmes, Edition Eyrolles 1995 Zbl1172.05001
  14. Prou J.-M., Wagneur E., Controllability in the max–algebra, In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997, revised version: Kybernetika 35 (1999), 13–24 (1997) MR1705527

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