Gradient observability for diffusion systems

El Hassane Zerrik; Hamid Bourray

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 2, page 139-150
  • ISSN: 1641-876X

Abstract

top
The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm illustrated by simulations.

How to cite

top

Zerrik, El Hassane, and Bourray, Hamid. "Gradient observability for diffusion systems." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 139-150. <http://eudml.org/doc/207629>.

@article{Zerrik2003,
abstract = {The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm illustrated by simulations.},
author = {Zerrik, El Hassane, Bourray, Hamid},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {gradient reconstruction; gradient strategic sensor; regional gradient observability; observability; diffusion system},
language = {eng},
number = {2},
pages = {139-150},
title = {Gradient observability for diffusion systems},
url = {http://eudml.org/doc/207629},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Zerrik, El Hassane
AU - Bourray, Hamid
TI - Gradient observability for diffusion systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 2
SP - 139
EP - 150
AB - The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm illustrated by simulations.
LA - eng
KW - gradient reconstruction; gradient strategic sensor; regional gradient observability; observability; diffusion system
UR - http://eudml.org/doc/207629
ER -

References

top
  1. Curtain R.F. and Zwart H. (1995): An Introduction to Infinite Dimensional Linear Systems Theory. - New York: Springer-Verlag. Zbl0839.93001
  2. Curtain R.F. and Pritchard A.J. (1978): Infinite Dimensional LinearSystems Theory. - New York: Springer. Zbl0426.93001
  3. Cuniasse-Langhans L. (1998): Evaluation par methode inversede la distribution des transferts de chaleur parietaux le long d'une plaque verticale en convection naturelle. - Ph.D. thesis, LETHEM INSA, Toulouse. 
  4. El Jai A. and Pritchard A.J. (1988): Sensors and Actuators in the Analysis of Distributed Systems. - New York: Wiley. Zbl0637.93001
  5. El Jai A. and El Yacoubi S. (1993): On the number of actuators in a parabolic system. - Appl. Math. Comp. Sci., Vol. 3, No. 4, pp. 673-686. Zbl0802.93033
  6. El Jai A., Simon M.C. and Zerrik E. (1993): Regional observability and sensor structures. - Int. J. Sens.Actuat., Vol. 39, No. 2, pp. 95-102. 
  7. El Jai A., Amouroux M. and Zerrik E. (1994): Regional observability of distributed systems. - Int. J. Syst.Sci., Vol. 25, No. 2, pp. 301-313. Zbl0812.93015
  8. Lions J.L. (1988): Contrôlabilite Exacte. - Paris: Masson. 
  9. Lions J.L. and Magenes E. (1968): Problemes aux Limites non Homogènes et Applications. - Paris: Dunod. Zbl0165.10801
  10. Sparrow E.M. (1963): On the calculation of radiant interchange between surfaces, In: Modern Developments in Heat Transfert (W. Ibele, Ed.). - New-York: Academic Press, pp. 181-212. 
  11. Zerrik E. (1993): Regional analysis of distributed parameter systems. - Ph.D. thesis, University MedV, Rabat, Morocco. 
  12. Zerrik E., Badraoui L. and El Jai A. (1999): Sensors and regional boundary state reconstruction of parabolic systems. - Sens. Actuat. J., Vol. 75, pp. 102-117. 
  13. Zerrik E., Boutoulout A. and Kamal A. (1999): Regional gradient controllability for parabolic systems. - Int. J.Appl. Math. Comp. Sci., Vol. 9, No. 4, pp. 767-787. Zbl1017.93013

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.