Reachability and observability of linear systems over max-plus

Michael J. Gazarik; Edward W. Kamen

Kybernetika (1999)

  • Volume: 35, Issue: 1, page [2]-12
  • ISSN: 0023-5954

Abstract

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This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable case, a duality is shown to exist between the two properties.

How to cite

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Gazarik, Michael J., and Kamen, Edward W.. "Reachability and observability of linear systems over max-plus." Kybernetika 35.1 (1999): [2]-12. <http://eudml.org/doc/33405>.

@article{Gazarik1999,
abstract = {This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable case, a duality is shown to exist between the two properties.},
author = {Gazarik, Michael J., Kamen, Edward W.},
journal = {Kybernetika},
keywords = {reachability; observability; linear system; max-plus algebra; reachability; observability; linear system; max-plus algebra},
language = {eng},
number = {1},
pages = {[2]-12},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Reachability and observability of linear systems over max-plus},
url = {http://eudml.org/doc/33405},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Gazarik, Michael J.
AU - Kamen, Edward W.
TI - Reachability and observability of linear systems over max-plus
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 1
SP - [2]
EP - 12
AB - This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable case, a duality is shown to exist between the two properties.
LA - eng
KW - reachability; observability; linear system; max-plus algebra; reachability; observability; linear system; max-plus algebra
UR - http://eudml.org/doc/33405
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. Cofer D., Garg V., Supervisory control of real–time discrete–event systems using lattice theory, IEEE Trans. Automat. Control 41 (1996), 199–209 (1996) Zbl0846.93005MR1375752
  3. Cohen G., Moller P., Quadrat J., Viot M., Algebraic tools for the performance evaluation of discrete event systems, Proc. IEEE 77 (1989), 39–58 (1989) 
  4. Cuninghame–Green R. A., Minimax Algebra, Springer Verlag, New York 1979 Zbl0739.90073MR0580321
  5. Doustmohammadi A., Kamen E., Direct generation of event–timing equations for generalized flow shop systems, In: Proceedings of the SPIE Photonics East 1995 Symposium, Philadelphia 1995, pp. 50–62 (1995) 
  6. Gazarik M., Monitoring and Control of Manufacturing Systems Based on the Max–plus Formulation, Ph.D. Thesis, Georgia Institute of Technology, Atlanta 1997 
  7. Gazarik M., Kamen E., Reachability and observability of linear systems over max–plus, In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997 MR1705526
  8. Kamen E. W., An Equation–based approach to the control of discrete event systems with applications to manufacturing, In: International Conference on Control Theory and Its Applications, Jerusalem 1993 
  9. Olsder G., Roos C., Cramer and Cayley–Hamilton in the max algebra, Linear Algebra Appl. 101 (1988), 87–108 (1988) Zbl0659.15012MR0941298
  10. 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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