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2011 | 21 | 3 | 499-508
Tytuł artykułu

Regional control problem for distributed bilinear systems: Approach and simulations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
21
Numer
3
Strony
499-508
Opis fizyczny
Daty
wydano
2011
otrzymano
2010-05-02
poprawiono
2010-11-23
poprawiono
2011-01-20
Twórcy
autor
  • MACS Team, Faculty of Sciences, Moulay Ismail University, BP 4010, Béni M'hamed, Zitoune, Meknes, Morocco
  • MACS Team, Faculty of Sciences, Moulay Ismail University, BP 4010, Béni M'hamed, Zitoune, Meknes, Morocco
  • TICOS Team, Faculty of Multidisciplinary Research, Moulay Ismail University, BP 512, Boutalamine, 52000, Errachidia, Morocco
Bibliografia
  • Ball, J.M., Marsden, J.E. and Slemrod, M. (1982). Controllability for distributed bilinear systems, SIAM Journal on Control and Optimization 20(4): 575-597.
  • 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.
  • 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).
  • 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.
  • Joshi, H.R. (2005). Optimal control of the convective velocity coefficient in a parabolic problem, Nonlinear Analysis 63 (5-7): 1383-1390.
  • Kato, T. (1995). Perturbation Theory for Linear Operators, Springer Verlag, Berlin/Heidelberg.
  • 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.
  • 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.
  • Khapalov, A.Y. (2010). Controllability of Partial Differential Equations Governed by Multiplicative Controls, Lecture Notes in Mathematics, Vol. 1995, Springer, Berlin, p. 284.
  • Lenhart, S. and Liang, M. (2000). Bilinear optimal control for a wave equation with viscous damping, Houston Journal of Mathematics 26(3): 575-595.
  • Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, NY.
  • Zerrik, E., Ouzahra, M. and Ztot, K. (2004). Regional stabilization for infinite bilinear systems, IEE: Control Theory and Applications 151(1): 109-116.
  • Zerrik, E. and Kamal, A. (2007). Output controllability for semi linear distributed parabolic system, Journal of Dynamical and Control Systems 13(2): 289-306.
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv21i3p499bwm
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