Regional detection and reconstruction of unknown internal or boundary sources

Larbi Afifi; Abdelhaq El Jai; Malika Merry

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 2, page 319-347
  • ISSN: 1641-876X

Abstract

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The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion system.

How to cite

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Afifi, Larbi, El Jai, Abdelhaq, and Merry, Malika. "Regional detection and reconstruction of unknown internal or boundary sources." International Journal of Applied Mathematics and Computer Science 11.2 (2001): 319-347. <http://eudml.org/doc/207509>.

@article{Afifi2001,
abstract = {The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion system.},
author = {Afifi, Larbi, El Jai, Abdelhaq, Merry, Malika},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {detection; sources; observation; region; sensors; regional detection; regionally detectable sources; spy sensors; strategic sensors; diffusion system},
language = {eng},
number = {2},
pages = {319-347},
title = {Regional detection and reconstruction of unknown internal or boundary sources},
url = {http://eudml.org/doc/207509},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Afifi, Larbi
AU - El Jai, Abdelhaq
AU - Merry, Malika
TI - Regional detection and reconstruction of unknown internal or boundary sources
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 2
SP - 319
EP - 347
AB - The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion system.
LA - eng
KW - detection; sources; observation; region; sensors; regional detection; regionally detectable sources; spy sensors; strategic sensors; diffusion system
UR - http://eudml.org/doc/207509
ER -

References

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  1. Afifi L. (1994): Analyse regionale: Systèmes distribues discrets and sources et detection. - Thèse d'etat, University of Kenitra, Morocco. 
  2. Afifi L. and El Jai A. (1994): Strategic sensors and spy sensors. - Appl. Math. Comp. Sci., Vol.4, No.4, pp.553-573. Zbl0823.93011
  3. Afifi L., El Jai A. and Merry M. (2000): Detection and sources reconstruction in a tube. - Int. J. Syst. Sci., Vol.31, No.2, pp.149-159. 
  4. Badraoui L., El Jai A. and Zerrik E. (1998): Sensors and regional boundary state. Reconstruction of parabolic systems. - Tech. Rep. No.1398, L.T.S., Universite de Perpignan, France, (to appear in Sensors and Actuators Journal). 
  5. Curtain R.F. and Zwart H. (1995): An Introduction to Infinite-Dimensional Linear Systems Theory. - New York: Springer. Zbl0839.93001
  6. Curtain R.F. and Pritchard A.J. (1978): Infinite Dimensional Linear Systems Theory. - Berlin: Springer. Zbl0389.93001
  7. El Jai A. and Berrahmoune L. (1984): Localisation d'actionneurs frontières pour la contrôlabilite de systèmes paraboliques. - C.R. Acad. Sc. Paris. Zbl0572.93005
  8. El Jai A. and Pritchard A.J., (1988): Sensors and Controls in the Analysis of Distributed Systems. - New York: Wiley. Zbl0637.93001
  9. El Jai A., Pritchard A.J., Simon M.C. and Zerrik E. (1995): Regional controllability of distributed systems. - Int. J. Contr., Vol. 26, No.6, pp.1351-1365. Zbl0844.93016
  10. El Jai A., Zerrik E. and Simon M.C. (1993): Regional observability and sensors structures. - Int. J. Sensors and Actuators, Vol.39, No.3, pp.95-102. 
  11. Isakov M. (1998): Inverse Problems for Partial Differential Equations. - New York: Springer. Zbl0908.35134
  12. Merry M. (2000): Detection et reconstruction de sources inconnues dans les systèmes distribues. - Ph.D. Thesis, Université Hassan II, Casablanca, Morocco. 
  13. Rafajłowicz E. (1984a): Optimization of actuators for distributed parameter systems identification. - Problems Contr. Inform. Theory, Vol.13, No.1, pp.9-51. Zbl0534.93064
  14. Rafajłowicz E. (1984b): Nonparametric algorithm for input signals identification in static distributed-parameter systems. - IEEE Trans. Automat. Contr., Vol. AC-29, No.7, pp.631-633. Zbl0542.93019
  15. Uciński D. (1992): Optimal sensors location for parameter identification of distributed systems. - Appl. Math. Comp. Sci., Vol.2, No.1, pp.119-134. Zbl0762.93022
  16. Zerrik E. (1993): Analyse regionale des systèmes distribues. - Thèse d'etat, Faculte des Sciences, Rabat, Morocco. 

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