# Linearization techniques for $\mathbb{L}^{\infty}$-control problems and dynamic programming principles in classical and $\mathbb{L}^{\infty}$-control problems

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LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : The aim of the paper is to provide a linearization approach to the $\mathbb{L}^{\infty}$-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the $\mathbb{L}^{p}$ approach and the associated linear formulations. This seems to be the most appropriate tool for treating $\mathbb{L}^{\infty}$ problems in continuous and lower semicontinuous setting.
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Journal articles
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https://hal-upec-upem.archives-ouvertes.fr/hal-00759482
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Submitted on : Friday, November 30, 2012 - 5:01:20 PM
Last modification on : Friday, August 5, 2022 - 2:41:30 PM

### Citation

Dan Goreac, Oana Silvia Serea. Linearization techniques for $\mathbb{L}^{\infty}$-control problems and dynamic programming principles in classical and $\mathbb{L}^{\infty}$-control problems. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2012, 18 (3), pp.836-855. ⟨10.1051/cocv/2011183⟩. ⟨hal-00759482⟩

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