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2010 | 20 | 2 | 227-238
Tytuł artykułu

Sensors and boundary state reconstruction of hyperbolic systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results are illustrated with numerical examples and simulations.
Rocznik
Tom
20
Numer
2
Strony
227-238
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-02-15
poprawiono
2009-10-22
Twórcy
  • MACS Group, Faculty of Sciences, University of Moulay Ismaïl, Bni Mhamed 4011, Meknes, Morocco
  • MACS Group, Faculty of Poly Disciplinary, University of Moulay Ismaïl, Boutalamine I, Errachidia, Morocco
  • Department of Mathematics, Faculty of Exact Sciences, Mentouri University, Constantine, Algeria
Bibliografia
  • Amouroux, A., El Jai, M. and Zerrik, E. (1994). Regional observability of distributed systems, International Journal of Systems Science 25(2): 301-313.
  • Avdonin, S.A. and Ivanov, S.A. (1995). Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems, Cambridge University Press, New York, NY/London/Melbourne.
  • Avdonin, S.A. and Ivanov, S.A. (1995). Boundary controllability problems for the wave equation in a parallelepiped, Applied Mathematic Letters 8(2): 97-102.
  • Avdonin, S.A., Ivanov, S.A. and Joó, I. (1995). Exponential series in the problem of initial and pointwise control of a rectangular vibrating membrane, Studia Scientiarium Mathematicarum Hungarica 30(3-4): 243-259.
  • Curtain, R.F. and Zwart, H. (1995). An Introduction to Infinite Dimensional Linear Systems Theory, Texts in Applied Mathematics, Vol. 21, Springer-Verlag, New York, NY.
  • Curtain, R.F. and Pritchard, A.J. (1978). Infinite Dimensional Linear Systems Theory, Springer-Verlag, New York, NY.
  • Dolecki, S. and Russel, D. (1977). A general theory of observation and control, SIAM Journal of Control 15(2): 185-220.
  • El Jai, A. and Pritchard, A.J. (1988). Sensors and Actuators in Distributed Systems Analysis, J. Wiley, New York, NY.
  • Kobayashi, T. (1980). Discrete-time observability for distributed parameter systems, International Journal of Control 31(1): 181-193.
  • Lions, J.L. and Magenes, E. (1968). Problèmes aux limites non homogènes et applications, Vols. 1 et 2, Dunod, Paris.
  • Lions, J.L. (1968). Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris.
  • Lions, J.L. (1988). Contrôlabilité Exacte. Perturbations et Stabilisation des Systèmes Distribués, Tome 1, Contrôlabilité Exacte, Masson, Paris.
  • Li, D., Gilliam, Z. and Martin, C. (1988). Discrete observavility of the heat equation on bounded domain, International Journal of Control 48(2): 755-780.
  • Micheletti, A. M. (1976). Perturbazione dello specttro di Un operatore ellitico di tipo variazionale, in relazione ad Una variazione del compo, Ricerche di matematica, V. XXV, Fasc. II.
  • Zerrik, E., Bourray, H. and Boutoulout, A. (2002). Regional boundary observability, numerical approach, International Journal of Applied Mathematics and Computer Science 12(2): 143-151.
  • Zerrik, E., Ben Hadid, S. and Bourray, H. (2007). Sensors and regional observability of hyperbolic systems, Sensors and Actuator Journal 138(2): 313-328.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv20i2p227bwm
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