An output controllability problem for semilinear distributed hyperbolic systems
Zerrik, E. ; Larhrissi, R. ; Bourray, H.
International Journal of Applied Mathematics and Computer Science, Tome 17 (2007), p. 437-448 / Harvested from The Polish Digital Mathematics Library
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The paper aims at extending the notion of regional controllability developed for linear systems cite 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.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:207848 
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     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},
     volume = {17},
     year = {2007},
     pages = {437-448},
     zbl = {1234.93023},
     language = {en},
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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) pp. 437-448. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv17i4p437bwm/

[000] Brezis H. (1993): Analyse fonctionnelle. Théorie et applications. -Paris: Masson. | Zbl 0511.46001

[001] Da Prato G., Prchard A. and Zabczyk J. (1991): On minimum energy problems. SIAM Journal on Control and Optimization, Vol.29, pp.209-221. | Zbl 0744.93098

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

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

[004] 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. | Zbl 0844.93016

[005] Fabre C., Puel J. P. and Zuazua E. (1995): Approximate controllability of the semilinear heat equation, Proceedings of the Royal Society of Edinburgh, Vol.125 A, pp.31-61. | Zbl 0818.93032

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

[007] Henry D. (1981): Geometric Theory of Semilinear Parabolic Systems. | Zbl 0456.35001

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

[009] Klamka J. (2002): Constrained exact controllability of semilinear systems. Systems and Control Letters, Vol.47, No.2, pp.139-147. | Zbl 1003.93005

[010] Klamka J. (2001): Constrained controllability of semilinear systems. Nonlinear Analysis, Vol.47, pp.2939-2949. | Zbl 1042.93504

[011] Klamka J. (2000): Schauder's fixed point theorem in nonlinear controllability problem. Control and Cybernetics, Vol.29, No.1, pp.153-165. | Zbl 1011.93001

[012] Klamka J. (1999): Constrained conllability of dynamical systems. International Journal of Applied Mathematics and Computer Science, Vol.9, No.2, pp.231-244. | Zbl 0959.93004

[013] Klamka J. (1998): Controllability of second order semilinear infinite-dimensional dynamical systems. Applied Mathematics and Computer Science, Vol.8, No.3, pp.459-470. | Zbl 0911.93015

[014] Klamka J. (1991): Controllability of Dynamical Systems, Dordrecht: Kluwer Academic Publishers. | Zbl 0732.93008

[015] Lions J.L. (1988): Contrôlabilité Exacte. Perturbations et Stabilisation des Systèmes Distribués, Tome 1, Contrôlabilité Exacte. -Paris: Masson. | Zbl 0653.93002

[016] Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations. -Berlin: Springer-Verlag. | Zbl 0516.47023

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

[018] Zuazua E. (1990): Exact controllability for the semilinear wave equation. Journal de Mathématiques Pures et Appliquées, 69, pp.1-31. | Zbl 0638.49017

[019] Zeidler E. (1999): Applied Functional Analysis. Applications to Mathematical Physics. - Springer. | Zbl 0834.46002

[020] 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. | Zbl 1049.93042

[021] 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. | Zbl 1036.49012

[022] 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. | Zbl 1011.93060

[023] Zerrik E., Boutoulout A. and El Jai A. (2000): Actuators and regional boundary controllability. International Journal of Systems Science, Vol.31, No.1 , pp.73-82 | Zbl 1080.93651