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IMA Journal of Mathematical Control and Information Advance Access originally published online on October 3, 2006
IMA Journal of Mathematical Control and Information 2007 24(3):371-382; doi:10.1093/imamci/dnl028
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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 the forward–backward heat coupled systems

René Dorville{dagger}

IUFM Guyane, Boulevard de la République, BP 6001, 97306 Cayenne Cedex, (FWI)

Abdennebi Omrane{ddagger}

Département de Mathématiques et Informatique, Université Antilles-Guyane, 97159 Pointe-à-Pitre, Guadeloupe (FWI)

{dagger} Email: dorville{at}guyane.iufm.fr

{ddagger} Corresponding author. Email: aomrane{at}univ-ag.fr

Received on December 7, 2005; Accepted on July 28, 2006

We give a singular optimality system for the control of the coupled (ill-posed) forward–backward heat problem using both the classical penalization method and the low-regret method of Lions (1992).

For the first method, we add the Slater hypothesis on the admissible closed convex set of controls Uad, while with the low-regret control method, we do not need this hypothesis.

Keywords: forward-backward heat system; ill-posed problems; optimal control; Slater hypothesis; penalization method; low-regret control; singular optimality system SOS.


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