Regional control problem for distributed bilinear systems: Approach and simulations

Karima Ztot; El Hassan Zerrik; Hamid Bourray

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 3, page 499-508
  • ISSN: 1641-876X

Abstract

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This paper investigates the regional control problem for infinite dimensional bilinear systems. We develop an approach that characterizes the optimal control and leads to a numerical algorithm. The obtained results are successfully illustrated by simulations.

How to cite

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Karima Ztot, El Hassan Zerrik, and Hamid Bourray. "Regional control problem for distributed bilinear systems: Approach and simulations." International Journal of Applied Mathematics and Computer Science 21.3 (2011): 499-508. <http://eudml.org/doc/208064>.

@article{KarimaZtot2011,
abstract = {This paper investigates the regional control problem for infinite dimensional bilinear systems. We develop an approach that characterizes the optimal control and leads to a numerical algorithm. The obtained results are successfully illustrated by simulations.},
author = {Karima Ztot, El Hassan Zerrik, Hamid Bourray},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {distributed systems; bilinear systems; regional controllability; regional optimal control problem},
language = {eng},
number = {3},
pages = {499-508},
title = {Regional control problem for distributed bilinear systems: Approach and simulations},
url = {http://eudml.org/doc/208064},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Karima Ztot
AU - El Hassan Zerrik
AU - Hamid Bourray
TI - Regional control problem for distributed bilinear systems: Approach and simulations
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 3
SP - 499
EP - 508
AB - This paper investigates the regional control problem for infinite dimensional bilinear systems. We develop an approach that characterizes the optimal control and leads to a numerical algorithm. The obtained results are successfully illustrated by simulations.
LA - eng
KW - distributed systems; bilinear systems; regional controllability; regional optimal control problem
UR - http://eudml.org/doc/208064
ER -

References

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  2. Bradley, M.E. and Lenhart, S. (2001). Bilinear spatial control of the velocity term in a Kirchhoff plate equation, Electronic Journal of Differental Equations (27): 1-15. Zbl0974.49012
  3. El Alami, N. (1988). Algorithms for implementation of optimal control with quadratic criterion of bilinear systems, in A. Bensoussan and J.L. Lions (Eds.) Analysis and Optimization of Systems, Lecture Notes in Control and Information Sciences, Vol. 111, Springer-Verlag, London, pp. 432-444, (in French). 
  4. El Jai, A., Simon, M.C., Zerrik, E. and Prirchard, A.J. (1995). Regional controllability of distributed parameter systems, International Journal of Control 62(6): 1351-1365. Zbl0844.93016
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  6. Kato, T. (1995). Perturbation Theory for Linear Operators, Springer Verlag, Berlin/Heidelberg. Zbl0836.47009
  7. Khapalov, A.Y. (2002a). Global non-negative controllability of the semilinear parabolic equation governed by bilinear control, ESAIM: Control, Optimisation and Calculus of Variations 7: 269-283. Zbl1024.93026
  8. Khapalov, A.Y. (2002b) On bilinear controllability of the parabolic equation with the reaction-diffusion term satisfying Newton's, Journal of Computational and Applied Mathematics 21: 1-23. Zbl1119.93017
  9. Khapalov, A.Y. (2010). Controllability of Partial Differential Equations Governed by Multiplicative Controls, Lecture Notes in Mathematics, Vol. 1995, Springer, Berlin, p. 284. Zbl1210.93005
  10. Lenhart, S. and Liang, M. (2000). Bilinear optimal control for a wave equation with viscous damping, Houston Journal of Mathematics 26(3): 575-595. Zbl0976.49005
  11. Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, NY. Zbl0516.47023
  12. Zerrik, E., Ouzahra, M. and Ztot, K. (2004). Regional stabilization for infinite bilinear systems, IEE: Control Theory and Applications 151(1): 109-116. 
  13. Zerrik, E. and Kamal, A. (2007). Output controllability for semi linear distributed parabolic system, Journal of Dynamical and Control Systems 13(2): 289-306. Zbl1119.93022
  14. Zerrik, E., Larhrissi, R. and Bourray, H. (2007). An output controllability problem for semi linear distributed hyperbolic system, International Journal of Applied Mathematics and Computer Science 17(4): 437-448, DOI: 10.2478/v10006007-0035-y. Zbl1234.93023

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