Regional control problem for distributed bilinear systems: approach and simulations

• Autorzy: Ztot K. , Zerrik E. H. , Bourray H.
• 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.

Słowa kluczowe

EN

distributed system; bilinear system; regional controllability; regional optimal control problem

PL

system rozproszony; system dwuliniowy; sterowalność regionalna; sterowanie optymalne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2011
• Tom: Vol. 21, no 3
• Strony: 499--508
• Opis fizyczny: Bibliogr. 14 poz., wykr.

Twórcy

autor

Ztot K.

autor

Zerrik E. H.

autor

Bourray H.

• MACS Team, Faculty of Sciences Moulay Ismail University, BP 4010, Béni M'hamed, Zitoune, Meknes, Morocco,

Bibliografia

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• [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.
• [5] Joshi, H. R. (2005). Optimal control of the convective velocity coefficient in a parabolic problem, Nonlinear Analysis 63 (5-7): 1383-1390.
• [6] Kato, T. (1995). Perturbation Theory for Linear Operators, Springer Verlag, Berlin/Heidelberg.
• [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.
• [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.
• [9] Khapalov, A. Y. (2010). Controllability of Partial Differential Equations Governed by Multiplicative Controls, Lecture Notes in Mathematics, Vol. 1995, Springer, Berlin, p. 284.
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• [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.
• [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/v10006-007-0035-y.