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2007 | 17 | 4 | 437-448
Tytuł artykułu

An output controllability problem for semilinear distributed hyperbolic systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
17
Numer
4
Strony
437-448
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-09-21
(nieznana)
2006-12-15
poprawiono
2007-09-11
Twórcy
autor
  • MACS Group-AFACS UFRi, Moulay Ismail University, Faculty of Sciences, Meknes, Meknes, Morocco
autor
  • MACS Group-AFACS UFRi, Moulay Ismail University, Faculty of Sciences, Meknes, Meknes, Morocco
autor
  • MACS Group-AFACS UFRi, Moulay Ismail University, Faculty of Sciences, Meknes, Meknes, Morocco
Bibliografia
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  • 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.
  • 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.
  • 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.
  • 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.
  • E. (1997): Null controllability of the proximate heat equation, ESAIM: Control Optimization and Calculus of Variations, Vol.2, pp.87-103.
  • Henry D. (1981): Geometric Theory of Semilinear Parabolic Systems.
  • 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.
  • Klamka J. (2002): Constrained exact controllability of semilinear systems. Systems and Control Letters, Vol.47, No.2, pp.139-147.
  • Klamka J. (2001): Constrained controllability of semilinear systems. Nonlinear Analysis, Vol.47, pp.2939-2949.
  • Klamka J. (2000): Schauder's fixed point theorem in nonlinear controllability problem. Control and Cybernetics, Vol.29, No.1, pp.153-165.
  • Klamka J. (1999): Constrained conllability of dynamical systems. International Journal of Applied Mathematics and Computer Science, Vol.9, No.2, pp.231-244.
  • Klamka J. (1998): Controllability of second order semilinear infinite-dimensional dynamical systems. Applied Mathematics and Computer Science, Vol.8, No.3, pp.459-470.
  • Klamka J. (1991): Controllability of Dynamical Systems, Dordrecht: Kluwer Academic Publishers.
  • Lions J.L. (1988): Contrôlabilité Exacte. Perturbations et Stabilisation des Systèmes Distribués, Tome 1, Contrôlabilité Exacte. -Paris: Masson.
  • Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations. -Berlin: Springer-Verlag.
  • Zeidler E. (1990): Nonlinear Functional Analysis and Its Applications II/A.Linear Applied Functional Analysis, Springer.
  • Zuazua E. (1990): Exact controllability for the semilinear wave equation. Journal de Mathématiques Pures et Appliquées, 69, pp.1-31.
  • Zeidler E. (1999): Applied Functional Analysis. Applications to Mathematical Physics. - Springer.
  • 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.
  • 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.
  • 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.
  • 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
Typ dokumentu
Bibliografia
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