Enlarged exact compensation in distributed systems

Larbi Afifi; Abdelhakim Chafiai; Abdelaziz Bel Fekih

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 4, page 467-477
  • ISSN: 1641-876X

Abstract

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In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study the relationship between the notion of remediability, introduced in previous works, and that of enlarged exact remediability.

How to cite

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Afifi, Larbi, Chafiai, Abdelhakim, and Bel Fekih, Abdelaziz. "Enlarged exact compensation in distributed systems." International Journal of Applied Mathematics and Computer Science 12.4 (2002): 467-477. <http://eudml.org/doc/207602>.

@article{Afifi2002,
abstract = {In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study the relationship between the notion of remediability, introduced in previous works, and that of enlarged exact remediability.},
author = {Afifi, Larbi, Chafiai, Abdelhakim, Bel Fekih, Abdelaziz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {distributed systems; sensors; control; actuators; remediability; disturbances; penalization; minimal energy; Hilbert uniqueness method},
language = {eng},
number = {4},
pages = {467-477},
title = {Enlarged exact compensation in distributed systems},
url = {http://eudml.org/doc/207602},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Afifi, Larbi
AU - Chafiai, Abdelhakim
AU - Bel Fekih, Abdelaziz
TI - Enlarged exact compensation in distributed systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 4
SP - 467
EP - 477
AB - In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study the relationship between the notion of remediability, introduced in previous works, and that of enlarged exact remediability.
LA - eng
KW - distributed systems; sensors; control; actuators; remediability; disturbances; penalization; minimal energy; Hilbert uniqueness method
UR - http://eudml.org/doc/207602
ER -

References

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  1. Afifi L., Chafiai A. and El Jai A. (1998): Compensation spatiale en temps fini dans les systèmes distribues. -Int. Rep., No. 14, L.T.S. Universite de Perpignan, France. 
  2. Afifi L., Chafiai A. and El Jai A. (1999): Regionally efficient and strategic actuators. -Int. J. Syst. Sci., (accepted). Zbl1013.93029
  3. Afifi L., Chafiai A. and El Jai A. (2000): Sensors and actuators for compensation in hyperbolic systems. -Proc. 14-th Int. Symp. Mathematical Theory of Networks and Systems, MTNS 2000, Perpignan, France, (CD-ROM). 
  4. Bel Fekih A. (1990): Une nouvelle approche pour l'analyse et le contrôle des systèmes distribues. -Thèse de doctorat d'etat, Faculte des sciences, Kenitra, Morocco. 
  5. Bergounioux M. (1994): Optimal control of parabolic problems with state constraints: A penalization method for optimality conditions. -Appl. Math. Optim., Vol. 29, No. 3, pp. 285-307. Zbl0813.49024
  6. Curtain R.F. and Pritchard A.J. (1978): Infinite Dimensional Linear Systems Theory. -New York: Springer. Zbl0389.93001
  7. Curtain R.F. and Zwart H. (1995): An Introduction to Infinite Dimensional Linear Systems Theory. -New York: Springer. Zbl0839.93001
  8. El Jai A. and Pritchard A.J. (1988): Sensors and Actuators in Distributed Systems Analysis. -New York: Wiley. Zbl0637.93001
  9. Lee E.B. and Marcus L. (1967): Foundation of Optimal Control Theory. -New York: Wiley. 
  10. Lions J.L. (1988): Contrôlabilite Exacte. -Paris: Masson. 
  11. Otsuka N. (1991): Simultaneous decoupling and disturbance rejection problemsfor infinite dimensional systems. -IMA J. Math. Contr. Inf., Vol. 8, pp. 165-178. Zbl0759.93019
  12. Rabah R. and Malabare M. (1997): A note on decoupling for linear infinite dimensional systems. -Proc. 4-th IFAC Conf. System Structure and Control, Bucharest, Romania, pp. 87-83. 

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