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IMA Journal of Mathematical Control and Information Advance Access originally published online on March 23, 2006
IMA Journal of Mathematical Control and Information 2007 24(1):1-12; doi:10.1093/imamci/dnl001
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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.

Optimal control for cooperative parabolic systems governed by Schrödinger operator with control constraints

G. M. Bahaa**

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

** Email: Bahaa_gm{at}hotmail.com


  Abstract

A distributed control problem for cooperative parabolic systems governed by Schrödinger operator is considered. The performance index is more general than the quadratic one and has an integral form. Constraints on controls are imposed. Making use of the Dubovitskii–Milyutin theorem given by Walczak (1984, One some control problems. Acta Univ. Lod. Folia Math., 1, 187–196), the optimality conditions are derived for the Dirichlet problem.

Keywords: cooperative parabolic systems; Schrödinger operator; existence of solution; optimal control; optimality conditions; Dubovitskii–Milyutin theorem; conical approximations; Weierstrass theorem.


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