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2010 | 20 | 3 | 427-443
Tytuł artykułu

Protector control: Extension to a class of nonlinear distributed systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a simulation example.
Rocznik
Tom
20
Numer
3
Strony
427-443
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-07-08
poprawiono
2010-03-24
Twórcy
  • MPPRN Laboratory, Faculty of Sciences and Techniques, B.P. 416, Tangier, Morocco
  • MPPRN Laboratory, Faculty of Sciences and Techniques, B.P. 416, Tangier, Morocco
Bibliografia
  • Afifi, L., Chafiai, A. and El Jai, A. (2002). Regionally efficient and strategic actuators, International Journal of Systems Science 33(4): 1-12.
  • Afifi, L., El Jai, A. and Merry, M. (2000). Detection and sources reconstruction in a tube, International Journal of Systems Science 31(2): 149-159.
  • Afifi, L., El Jai, A. and Merry, M. (2001). Regional detection and reconstruction of unknown internal or boundary sources, International Journal of Applied Mathematics and Computer Science 11(2): 319-348.
  • Beltrami, E. (1987). Mathematics for Dynamic Modelling, Academic Press, San Diego, CA.
  • Bernoussi, A. (2007). Spreadability and vulnerability of distributed parameter systems, International Journal of Systems Science 38(4): 305-317.
  • Bernoussi, A. and Amharref, M. (2003). Etalabilité-vulnrabilité, Annals of University of Craiova, Mathematics and Computer Science Series 30(4): 53-62.
  • Bernoussi, A. and El Jai, A. (2000). New approach of spreadability, Journal of Mathematical and Computer Modelling 31(13): 93-109.
  • Bernoussi, A., El Jai, A. and Pritchard, A. J. (2001). Spreadability and evolving interfaces, International Journal of Systems Science 32(10): 1217-1232.
  • Bernoussi, A. (2010). Spreadability, vulnerability and protector control, Mathematical Modelling of Natural Phenomena 5(7): 145-150, DOI: 10.1051/mmnp/20105724.
  • Curtain, R.F. and Pritchard, A.J. (1978). Infinite Dimensional Linear Systems Theory, Springer, Berlin.
  • Dautray, R.F. and Lions, J.. (1984). Analyse mathématique et calcul numérique pour les sciences et les techniques, Série Scientifique, Tome 3, Masson, Paris.
  • Diaz, J.I. and Lions, J. L. (1993). Mathematics Climate and Environment, Research in Applied Mathematics, RMA 27, Masson, Paris.
  • El Jai, A. (2002). Analyse régionale des systémes distribuès, SMAI (Société de Mathématiques Appliquées et Industrielles), ESAIM-European Series in Applied and Industrial Mathematics 8: 663-692.
  • El Jai, A. (2004). Eléments d'Analyse et Contrôle des Systèmes, Collection études, University of Perpignan Press, Perpignan.
  • El Jai, A. and Kassara, K. (1994). Spreadable distributed systems, Mathematical and Computer Modelling 20(1): 47-64.
  • El Jai, A. and Kassara, K. (1996). Spreadability of transport systems, International Journal of Systems Science 27(7): 681-688.
  • El Jai, A. and Pritchard, A.J. (1986). Capteurs et actionneurs dans l'analyse des systems distribués, RMA 3, Masson, Paris.
  • El Jai, A., Simon, M., Zerrik, E. and Pritchard, A.J. (1995). Regional controllability of distributed systems, International Journal of Control 62(6): 1351-1365.
  • Giuggioli, L. and Kenkre, V.M. (2003). Analytic solutions of a nonlinear convective equation in population dynamics, Physica D 183: 245-259.
  • Henry, D. (1981). Geometric Theory of Semilinear Parabolic Systems, Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin/New York, NY.
  • Ichikawa, A. (1982). Quadratic control of evolution equations with delays in control, SIAM Journal Control and Optimization 20(5): 645-668.
  • Kenkre, V.M. (2004). Results from variants of the Fisher equation in the study of epidemics and bacteria, Physica A 342: 242-248.
  • Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol. 44, Springer-Verlag, New York, NY, Berlin/Heidelberg/Tokyo.
  • Qaraai, Y. (2008). Compensation des perturbations étalables et contrôle protecteur des zones vulnrables, Ph.D. thesis, Faculty of Sciences and Techniques of Tangier, Morocco.
  • Qaraai, Y., Bernoussi, A. and El Jai, A. (2006). Contrôle protecteur et remdiabilité, Proceeding of the 3rd International Congress on Scientific Advances in Civil and Industrial Engineering, Algeciras, Spain, pp. 108-114.
  • Qaraai, Y., Bernoussi, A. and El Jai, A. (2008). How to compensate a spreading disturbance for a class of nonlinear systems, International Journal Applied Mathematics and Computer Science 18(2): 171-187, DOI: 10.2478/v10006008-0016-9.
  • Qaraai, Y., Bernoussi, A. and El Jai, A. (2009). Protector control for a class of nonlinear systems, Proceeding of the International Conference on Systems Theory: Modeling, Analysis and Control, Fes2009, Fes, Morocco, pp. 265-272.
  • Smart, D.R. (1994). Fixed Point Theorems, Cambridge University Press, London.
  • Zerrik, E., El Jai, A. and Amouroux, M. (1994). Regional observability of distributed systems, International Journal of Systems Science 25(6): 301-313.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv20i3p427bwm
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