SUPERVISORY CONTROL OF HEAP MODELS USING SYNCHRONOUS COMPOSITION

Jan Komenda, Jean-Louis Boimond, Sébasten Lahaye

Abstract

Heaps models are powerful models for concurrent timed discrete event systems. They admit linear description using dioid algebras. Inspired by supervisory control of logical discrete event systems we introduce parallel composition of heap models, called synchronous product, to formally describe the action of supervisor (represented by another heap model) on the system. This additional explicit concurrency for naturally concurrent heap models is useful for studying supervisory control in the algebraic framework of dioid algebras. Timing aspects of supervisory control, i.e. optimal timing of the controller, is studied based on residuation theory.

References

  1. M. Al Saba, J.L. Boimond, and S. Lahaye. On just in time control of flexible manufacturing systems via dioid algebra. Proceedings of INCOM'06, Saint-Etienne, France, vol.2, pp. 137-142, 2006.
  2. F. Baccelli, G. Cohen, G.J. Olsder and J.P.Quadrat (1992). Synchronization and linearity. An algebra for discrete event systems. New York, Wiley.
  3. B. Cottenceau, L. Hardouin, J.L. Boimond, and J.L. Ferrier. Model Reference Control for Timed Event Graphs in Dioid, Automatica, vol. 37, pp. 1451-1458, 2001.
  4. S. Gaubert. Théorie des systèmes linéaires dans les dioïdes. Thèse de doctorat, Ecole des Mines de Paris, 1992.
  5. S. Gaubert. Performance evaluation of (max,+) automata, IEEE Trans. on Automatic Control, 40(12), pp. 2014- 2025, 1995.
  6. S. Gaubert and J. Mairesse. Task resource models and (max,+) automata, In J. Gunawardena, Editor: Idempotency. Cambridge University Press, 1997.
  7. S. Gaubert and J. Mairesse. Modeling and analysis of timed Petri nets using heaps of pieces. IEEE Trans. on Automatic Control, 44(4): 683-698, 1999.
  8. J.R. Jackson. Scheduling a Production Line to Minimize Maximum Tardiness. Research report 43. University of California Los Angeles. Management Science Research Project.
  9. J.Komenda, M.Al Saba, and J.L. Boimond. Supervisory Control of Maxplus Automata: Quantitative Aspects. In Proceedings ECC 2007, Kos (Greece).
  10. R. Kumar, M. Heymann. Masked prioritized synchronization for interaction and control of discrete-event systems, IEEE Transaction Automatic Control 45, 1970- 1982, 2000.
  11. F. Lin and W.M. Wonham, On Observability of DiscreteEvent Systems, Information Sciences, 44: 173-198, 1
  12. E. Menguy. Contribution à la commande des systèmes linaires dans les diodes. Thèse de doctorat, Université d'Angers, 1997.
  13. P.J. Ramadge and W.M. Wonham. The Control of DiscreteEvent Systems. Proc. IEEE, 77:81-98, 1989.
  14. J. Sifakis and S. Yovine. Compositional specification of timed systems. Proceedings of the 13th Symp. on Theoretical Aspects of Computer Science, STACS'96, pp. 347-359, 1996. LNCS 1046.
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Paper Citation


in Harvard Style

Komenda J., Boimond J. and Lahaye S. (2007). SUPERVISORY CONTROL OF HEAP MODELS USING SYNCHRONOUS COMPOSITION . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: From Planning to Control of Manufacturing Systems, (ICINCO 2007) ISBN 978-972-8865-82-5, pages 467-475. DOI: 10.5220/0001636104670475


in Bibtex Style

@conference{from planning to control of manufacturing systems07,
author={Jan Komenda and Jean-Louis Boimond and Sébasten Lahaye},
title={SUPERVISORY CONTROL OF HEAP MODELS USING SYNCHRONOUS COMPOSITION},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: From Planning to Control of Manufacturing Systems, (ICINCO 2007)},
year={2007},
pages={467-475},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001636104670475},
isbn={978-972-8865-82-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: From Planning to Control of Manufacturing Systems, (ICINCO 2007)
TI - SUPERVISORY CONTROL OF HEAP MODELS USING SYNCHRONOUS COMPOSITION
SN - 978-972-8865-82-5
AU - Komenda J.
AU - Boimond J.
AU - Lahaye S.
PY - 2007
SP - 467
EP - 475
DO - 10.5220/0001636104670475