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IMA Journal of Mathematical Control and Information Advance Access originally published online on November 6, 2008
IMA Journal of Mathematical Control and Information 2008 25(4):491-505; doi:10.1093/imamci/dnn005
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Boundary control for hyperbolic systems involving infinite-order operators with control constraints

G. M. Bahaa{dagger}

Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

{dagger} Email: bahaa_gm{at}hotmail.com

Received on May 23, 2007; Revision received January 29, 2008. Accepted on April 5, 2008

In this paper, a class of n x n hyperbolic boundary control problems with control constraints is investigated. We first establish the solvability of an n x n system with non-homogeneous mixed Neumann conditions involving hyperbolic operator of infinite order. Also a boundary control problem for this system is considered. The necessary and sufficient conditions for the control to be optimal are obtained. Two mathematical examples for derived optimality conditions are presented.

Keywords: boundary control problems; n x n hyperbolic system; Neumann conditions; existence and uniqueness of solution; infinite-order operator.


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