How to compensate a spreading disturbance for a class of nonlinear systems
Youssef Qaraai ; Abdes Samed Bernoussi ; Abdelhaq El Jai
International Journal of Applied Mathematics and Computer Science, Tome 18 (2008), p. 171-187 / Harvested from The Polish Digital Mathematics Library

We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:207875
@article{bwmeta1.element.bwnjournal-article-amcv18i2p171bwm,
     author = {Youssef Qaraai and Abdes Samed Bernoussi and Abdelhaq El Jai},
     title = {How to compensate a spreading disturbance for a class of nonlinear systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {18},
     year = {2008},
     pages = {171-187},
     zbl = {1234.93077},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv18i2p171bwm}
}
Youssef Qaraai; Abdes Samed Bernoussi; Abdelhaq El Jai. How to compensate a spreading disturbance for a class of nonlinear systems. International Journal of Applied Mathematics and Computer Science, Tome 18 (2008) pp. 171-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv18i2p171bwm/

[000] Afifi L., El Jai A. and Zerrik E.(2008). Analyse régionale des systèmes linéaires à paramétres distribués, Press Universitaires de Perpignan, In press.

[001] Afifi L., A. Chafiai and A. El Jai (2002). Regionally efficient and strategic actuators, International Journal of Systems Science 33 (4): 1-12. | Zbl 1013.93029

[002] Bernoussi A. (2007). Spreadability and vulnerability of distributed parameter systems, International Journal of Systems Science 38(4): 305-317. | Zbl 1115.93007

[003] Bernoussi A. and A. El Jai, (2000). New approach of spreadability, Journal of Mathematical and Computer Modelling 31(13): 93-109. | Zbl 0960.93018

[004] Bernoussi A., A. El Jai and A. J. Pritchard (2001). Spreadability and evolving interfaces, International Journal of Systems Science 32(10): 1217-1232. | Zbl 1014.93015

[005] Bernoussi A. and M. Amharref (2003). Etalabilité-vulnérabilité, Annals of University of Craiova, Mathematics and Computer Science Series 30: 53-62. ISSN 1223-6934.

[006] Cholewa J. W. and T. Dłotko (2000). Global Attractors in Abstract Parabolic Problems, Cambridge University Press, London Mathematical Society. | Zbl 0954.35002

[007] Christofides P. D. (1998). Robust control of parbolic PDE Systems, Chemical Engineering Science 53: 2949-2965.

[008] Christofides P.D. and P. Daoutidis (1998). Robust control of hyperbolic PDE systems, Chemical Engineering Science 53: 85-105. | Zbl 0981.93045

[009] Christofides P.D. (2001). Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes, Springer, Berkhäuser. | Zbl 1018.93001

[010] Curtain R. F. and A.J. Pritchard (1978). Infinite Dimensional Linear Systems Theory, Springer, Berlin-Heidelberg, New York, pp. 297. | Zbl 0389.93001

[011] Dautray R. F. and J. L. Lions (1984). Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 3, Masson, Paris. | Zbl 0642.35001

[012] Doubova A., E. Fernández-Cara, M. González-Burgos and E. Zuazua (2006). On the controllability of parabolic systems with a nonlinear term involving the state and the gradient, SIAM Journal on Control and Optimization 45(4): 1399-1446. | Zbl 1038.93041

[013] El Jai A. and A. J. Pritchard (1986). Capteurs et actionneurs dans l'analyse des systems distribués, Masson, Paris. | Zbl 0627.93001

[014] El Jai A. and K. Kassara (1994). Spreadable distributed systems. Mathematical and Computer Modelling 20(1): 47-64. | Zbl 0829.92018

[015] El Jai A., M.C. Simon, E. Zerrik and A.J. Pritchard (1995). Regional controllability of distributed systems, International Journal of Control 62(6): 1351-1365. | Zbl 0844.93016

[016] El Jai A. (2002). Analyse régionale des systémes distribués, ESAIM: Control, Optimisation and Calculus of Variations 8: 663-692.

[017] El Jai A. (2004). Eléments d'Analyse et de Contrôle des Systémes, Presses Universitaires de Perpignan.

[018] Henry D. (1981). Geometric Theory of Semilinear Parabolic Systems, Springer, New York. | Zbl 0456.35001

[019] Kassara K. and A. El Jai (1983). Algorithmes pour la commande d'une classe de systems à paramètres répartis non linéaires, Revue Marocaine d'Automatique, d'Informatique et de Traitement de Signal 1(1): 3-24.

[020] Pazy A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York. | Zbl 0516.47023

[021] Qaraai Y., A. Bernoussi and A. El Jai (2006). Contrôle protecteur et remédiabilité, Proceedings of the 3rd International Congress on Scientific Advances in Civil and Industrial Engineering, Algeciras, Spain, pp. 107-114.

[022] Qaraai Y., A. Bernoussi and A. El Jai (2008). Protector control of distributed parameter systems, International Journal of Systems Science, submitted. | Zbl 1234.93077