Regional Gradient Controllability of Semi-Linear Parabolic Systems

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


The purpose of this paper is to study regional gradient controllability for a class of semi-linear distributed parabolic systems. First, we give a definition and delineate some properties of this concept, and we show that under the hypothesis, the approximate regional gradient controllability of semi-linear parabolic system, we find a control which steers a system to a desired gradient in a sub-region of the system domain. At last, we present an approach based on fixed point techniques leading to a numerical approach which is successfully tested through various examples and simulations.
Copyright © 2013 Praise Worthy Prize - All rights reserved.


Template Gradient; Semi-Linear Parabolic Systems; Regional Controllability; Fixed-Point Theorems

Full Text:



Klamka J., Controllability of dynamical systems. Mathematics and its applications. Vol. 48, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.

Klamka J., Constrained controllability of nonlinear systems. Journal of Mathematical Analysis and Applications. Vol. 201, N 2, 1996, pp. 365-374.

Klamka J., Schauder's fixed point theorem in nonlinear controllability problems. Control and Cybernetics. Vol. 29, N 3, 2000, pp. 377-393.

A. El Jai and A.J. Pritchard, Capteurs et actionneurs dans l'analyse des systèmes distribués. Masson. RMA 3. Paris. 1986.

A. El Jai, A.J. Pritchard, M.C. Simon, and E. Zerrik, Regional controllability of distributed systems. International Journal of Control, Vol. 62, N 6, 1351-1365, 1995.

E. Zerrik, A. Boutoulout and A. El Jai, Actuators and regional boundary controllability of parabolic systems. International Journal of Systems Science, Vol. 31, N 1, 73-82, 2000.

E. Zerrik and A. Kamal, Output controllability for semi-linear distributed parabolic systems. Journal of Dynamical and Control Systems, Vol. 13, N 2, 289-306, April 2007.

Zerrik E., Boutoulout A. and Kamal A., Regional gradient controllability for parabolic systems. Int. J. Appl. Math. Comp. Sci., Vol. 9, N 4, 1999, pp. 767-787.

J.L. Lions, Contrôlabilité exacte. Perturbations et stabilisation des systèmes distribués. Tome 1, Contrôlabilité Exacte 1988, Masson.

A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New-York, 1983.

H. Brezis, Analyse fonctionnelle : théorie et application, Masson, 1983.

E. Zeidler, Applied functional analysis : Applications to mathematical physics. Vol. 108. Springer-Verlag, New-York, 1995.

Kamal A., Boutoulout A., Ould Beinane S. A., Regional boundary controllability of semi-linear distributed parabolic system, (2010) International Review of Automatic Control (IREACO), 3 (4), pp. 378-387.

K. Kassara and A. El Jai, Algorithme pour la commande d'une classe de systèmes à paramétres répartis non linéaires. Rev. Mar. d'aut. d'inf. de Trait. de signal. Vol. 1, N 1, 3-24, 1993.

F. De Souza J.A.M and Pritchard A.J., Control of semi-linear distributed parameter systems. Telecomunication and Control, INPE Press, Sao Jose dos Campos, Brasil, 1985, pp. 202-207.

A. Kamal, A. Boutoulout and S. Beinane, "Regional Controllability of Semi-Linear Distributed Parabolic Systems: Theory and Simulation," Intelligent Control and Automation, Vol. 3 No. 2, 2012, pp. 146-158.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2023 Praise Worthy Prize