Geodesic
An output controllability problem for semilinear distributed hyperbolic systems
International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 4, pp. 437-446.

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

The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.
Keywords: distributed-parameter systems, semilinear hyperbolic systems, constrained controllability, fixed point
Mots-clés : system o parametrach rozłożonych, system półliniowy, system hyperboliczny, sterowność wymuszona, punkt stały 
@article{IJAMCS_2007_17_4_a0,
     author = {Zerrik, E. and Larhrissi, R. and Bourray, H.},
     title = {An output controllability problem for semilinear distributed hyperbolic systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {437--446},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2007_17_4_a0/}
}
TY  - JOUR
AU  - Zerrik, E.
AU  - Larhrissi, R.
AU  - Bourray, H.
TI  - An output controllability problem for semilinear distributed hyperbolic systems
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2007
SP  - 437
EP  - 446
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2007_17_4_a0/
LA  - en
ID  - IJAMCS_2007_17_4_a0
ER  - 
%0 Journal Article
%A Zerrik, E.
%A Larhrissi, R.
%A Bourray, H.
%T An output controllability problem for semilinear distributed hyperbolic systems
%J International Journal of Applied Mathematics and Computer Science
%D 2007
%P 437-446
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2007_17_4_a0/
%G en
%F IJAMCS_2007_17_4_a0
Zerrik, E.; Larhrissi, R.; Bourray, H. An output controllability problem for semilinear distributed hyperbolic systems. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 4, pp. 437-446. http://geodesic.mathdoc.fr/item/IJAMCS_2007_17_4_a0/

[1] Brezis H. (1993): Analyse fonctionnelle. Théorie et applications. - Paris: Masson.

[2] Da Prato G. , Pritchard A. and Zabczyk J. (1991): On minimum energy problems. SIAM Journal on Control and Optimization, Vol. 29, pp. 209-221.

[3] De Souza F., J.A.M., and A.J.Pritchard (1985): Control of semilinear distributed parameter systems. Telecommunication and Control, INPE, Sao José dos Campos, Brazil, pp. 160-164.

[4] De Souza F. J.A.M (1985): Control of nonlinear ditributed parameter systems. In: Proc. IV Coloquio de Control Automatico (Ibarra-Zannatha, Ed.), Centro de investigation y Estudios Avanzados del instituto Politecnico Nacional de Mexico, Mexico, Vol. 1 , pp. 37-43.

[5] El Jai A., Zerrik E., Simon M. C. and Pritchard A. J. (1995): Regional controllability of distributed parameter systems. International Journal of Control, Vol. 62, No. 6, pp. 1351-1365.

[6] Fabre C. , Puel J. P. and Zuazua E. (1995): Approximate controllabiliy of the semilinear heat equation, Proceedings of the Royal Society of Edinburgh, Vol. 125 A, pp. 31-61.

[7] E. (1997): Null controllability of the proximate heat equation, ESAIM: Control Optimization and Calculus of Variations, Vol. 2, pp. 87-103.

[8] Henry D. (1981): Geometric Theory of Semilinear Parabolic Systems.

[9] Kassara K. and El Jaï A. (1983): Algorithme pour la commande d'une classe de systèmes à paramètres répartis non linéaires. Revue marocaine d'automatique, d'informatique et de traitement de signal, Vol. 1, No. 2, pp. 95-117.

[10] Klamka J. (2002): Constrained exact controllability of semilinear systems. Systems and Control Letters, Vol. 47, No. 2, pp. 139-147.

[11] Klamka J. (2001): Constrained controllability of semilinear systems. Nonlinear Analysis, Vol. 47, pp. 2939-2949.

[12] Klamka J. (2000): Schauder's fixed point theorem in nonlinear controllability problem. Control and Cybernetics, Vol. 29, No. 1, pp. 153-165.

[13] Klamka J. (1999): Constrained conllability of dynamical systems. International Journal of Applied Mathematics and Computer Science, Vol. 9, No. 2, pp. 231-244.

[14] Klamka J. (1998): Controllability of second order semilinear infinite-dimensional dynamical systems. Applied Mathematics and Computer Science, Vol. 8, No. 3, pp. 459-470.

[15] Klamka J. (1991): Controllability of Dynamical Systems, Dordrecht: Kluwer Academic Publishers.

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

[17] Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations.-Berlin: Springer-Verlag.

[18] Zeidler E. (1990): Nonlinear Functional Analysis and Its Applications II/A. Linear Applied Functional Analysis, Springer.

[19] Zuazua E. (1990): Exact controllability for the semilinear wave equation. Journal de Mathématiques Pures et Appliquées, 69, pp. 1-31.

[20] Zeidler E. (1999): Applied Functional Analysis. Applications to Mathematical Physics.- Springer.

[21] Zerrik E., Bourray H. and El Jai A. (2004): Regional observability of semilinear distributed parabolic systems. International Journal of Dynamical and Control Systems, Vol. 10, No. 3, pp. 413-430.

[22] Zerrik E. and Larhrissi R. (2002): Regional boundary controllability of hyperbolic systems. Numerical approach. International Journal of Dynamical and Control Systems, Vol. 8, No. 3, pp. 293-311.

[23] Zerrik E. and Larhrissi R. (2001): Regional Target Control of the wave Equation. International Journal of Systems Science, Vol. 32, No. 10, pp. 1233-1242.

[24] Zerrik E., Boutoulout A. and El Jaï A. (2000): Actuators and regional boundary controllability. International Journal of Systems Science, Vol. 31, No. 1 , pp. 73-82.