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IMA Journal of Mathematical Control and Information Advance Access originally published online on June 28, 2006
IMA Journal of Mathematical Control and Information 2007 24(2):149-161; doi:10.1093/imamci/dnl018
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Distributed control for cooperative systems involving parabolic operators with an infinite number of variables

H. M. Serag**

Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt

** Email: serraghm{at}yahoo.com


  Abstract

The optimal control for cooperative systems involving parabolic operators with an infinite number of variables is considered. First the existence and uniqueness of the states are proved; then the necessary and sufficient condition for the control to be optimal is obtained by a set of inequalities. The control in our problems is of distributed type and is allowed to be in the Hilbert space (L2(0, T, L2(R{infty})))n.

Keywords: cooperative systems with Dirichlet and Neumann conditions; existence and uniqueness of solutions; parabolic operators with an infinite number of variables; distributed control problems.

Received on 18 May 2005.


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