Geodesic
Sensors and boundary state reconstruction of hyperbolic systems
International Journal of Applied Mathematics and Computer Science, Tome 20 (2010) no. 2, pp. 227-238.

Voir la notice de l'article provenant de la source Library of Science

This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results are illustrated with numerical examples and simulations.
Keywords: distributed system, hyperbolic system, regional observability, boundary reconstruction, strategic sensor
Mots-clés : system rozproszony, system hyperboliczny, czujnik strategiczny 
@article{IJAMCS_2010_20_2_a0,
     author = {Zerrik, E. H. and Bourray, H. and Ben Hadid, S.},
     title = {Sensors and boundary state reconstruction of hyperbolic systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {227--238},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_2_a0/}
}
TY  - JOUR
AU  - Zerrik, E. H.
AU  - Bourray, H.
AU  - Ben Hadid, S.
TI  - Sensors and boundary state reconstruction of hyperbolic systems
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2010
SP  - 227
EP  - 238
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_2_a0/
LA  - en
ID  - IJAMCS_2010_20_2_a0
ER  - 
%0 Journal Article
%A Zerrik, E. H.
%A Bourray, H.
%A Ben Hadid, S.
%T Sensors and boundary state reconstruction of hyperbolic systems
%J International Journal of Applied Mathematics and Computer Science
%D 2010
%P 227-238
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_2_a0/
%G en
%F IJAMCS_2010_20_2_a0
Zerrik, E. H.; Bourray, H.; Ben Hadid, S. Sensors and boundary state reconstruction of hyperbolic systems. International Journal of Applied Mathematics and Computer Science, Tome 20 (2010) no. 2, pp. 227-238. http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_2_a0/

[1] Amouroux, A., El Jai, M. and Zerrik, E. (1994). Regional observability of distributed systems, International Journal of Systems Science 25(2): 301-313.

[2] Avdonin, S.A. and Ivanov, S.A. (1995). Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems, Cambridge University Press, New York, NY/London/Melbourne.

[3] Avdonin, S.A. and Ivanov, S.A. (1995). Boundary controllability problems for the wave equation in a parallelepiped, Applied Mathematic Letters 8(2): 97-102.

[4] Avdonin, S.A., Ivanov, S.A. and Joó, I. (1995). Exponential series in the problem of initial and pointwise control of a rectangular vibrating membrane, Studia Scientiarium Mathematicarum Hungarica 30(3-4): 243-259.

[5] Curtain, R.F. and Zwart, H. (1995). An Introduction to Infinite Dimensional Linear Systems Theory, Texts in Applied Mathematics, Vol. 21, Springer-Verlag, New York, NY.

[6] Curtain, R.F. and Pritchard, A.J. (1978). Infinite Dimensional Linear Systems Theory, Springer-Verlag, New York, NY.

[7] Dolecki, S. and Russel, D. (1977). A general theory of observation and control, SIAM Journal of Control 15(2): 185-220.

[8] El Jai, A. and Pritchard, A.J. (1988). Sensors and Actuators in Distributed Systems Analysis, J. Wiley, New York, NY.

[9] Kobayashi, T. (1980). Discrete-time observability for distributed parameter systems, International Journal of Control 31(1): 181-193.

[10] Lions, J.L. and Magenes, E. (1968). Problèmes aux limites non homogènes et applications, Vols. 1 et 2, Dunod, Paris.

[11] Lions, J.L. (1968). Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris.

[12] Lions, J.L. (1988). Contrôlabilité Exacte. Perturbations et Stabilisation des Systèmes Distribués, Tome 1, Contrôlabilité Exacte, Masson, Paris.

[13] Li, D., Gilliam, Z. and Martin, C. (1988). Discrete observavility of the heat equation on bounded domain, International Journal of Control 48(2): 755-780.

[14] Micheletti, A. M. (1976). Perturbazione dello specttro di Un operatore ellitico di tipo variazionale, in relazione ad Una variazione del compo, Ricerche di matematica, V. XXV, Fasc. II.

[15] Zerrik, E., Bourray, H. and Boutoulout, A. (2002). Regional boundary observability, numerical approach, International Journal of Applied Mathematics and Computer Science 12(2): 143-151.

[16] Zerrik, E., Ben Hadid, S. and Bourray, H. (2007). Sensors and regional observability of hyperbolic systems, Sensors and Actuator Journal 138(2): 313-328.