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Optimal Control of Ill-Posed Parabolic Distributed Systems

In: Mathematical Modeling, Simulation, Visualization and e-Learning

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  • A. Omrane

Abstract

We show that the low-regret notion of Lions [C. R. Acad. Sci. Paris Ser. I Math. 315:1253–1257, 1992] is well adapted for the control of the ill-posed heat problem. Passing to the limit, we give a characterization of the no-regret control by a singular optimality system. No Slater hypothesis on the admissible set of controls u ad is necessary, since we use a corrector of order zero argument. The result is a generalization of the low-regret control [Dorville et al., Appl. Math. Lett. 17:549–552, 2004; Dorville et al., C. R. Acad. Sci. Paris Ser. I Math. 338:921–924, 2004] to the no-regret control optimality system.

Suggested Citation

  • A. Omrane, 2008. "Optimal Control of Ill-Posed Parabolic Distributed Systems," Springer Books, in: Dialla Konaté (ed.), Mathematical Modeling, Simulation, Visualization and e-Learning, pages 165-179, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74339-2_10
    DOI: 10.1007/978-3-540-74339-2_10
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