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IMA Journal of Mathematical Control and Information Advance Access published online on October 3, 2006
IMA Journal of Mathematical Control and Information, 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.
Received December 7, 2005
Accepted July 28, 2006

Article

Optimal control for the forward-backward heat coupled systems

René Dorville 1 and Abdennebi Omrane 2 *

1 IUFM Guyane, Boulevard de la République, BP 6001, 97306 Cayenne Cedex, (FWI)
2 Département de Mathématiques et Informatique, Université Antilles-Guyane, 97159 Pointe-à-Pitre, Guadeloupe (FWI)

* To whom correspondence should be addressed.
Abdennebi Omrane, E-mail: aomrane{at}univ-ag.fr


  Abstract

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 {Uscript}ad, 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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