The aim of the paper is to provide a linearization approach to the ${\mathbb{L}}^{\infty}$See PDF-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 ${\mathbb{L}}^{p}$See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating ${\mathbb{L}}^{\infty}$See PDF problems in continuous and lower semicontinuous setting.

Keywords: dynamic programming principle, essential supremum, hj equations, occupational measures, $\mathbb {L}^{p}$See pdf approximations

@article{COCV_2012__18_3_836_0, author = {Goreac, Dan and Serea, Oana-Silvia}, title = {Linearization techniques for $\mathbb {L}^{\infty }${See} {PDF-control} problems and dynamic programming principles in classical and $\mathbb {L}^{\infty }${See} {PDF-control} problems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {836--855}, publisher = {EDP-Sciences}, volume = {18}, number = {3}, year = {2012}, doi = {10.1051/cocv/2011183}, mrnumber = {3041666}, zbl = {1262.49030}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2011183/} }

TY - JOUR AU - Goreac, Dan AU - Serea, Oana-Silvia TI - Linearization techniques for $\mathbb {L}^{\infty }$See PDF-control problems and dynamic programming principles in classical and $\mathbb {L}^{\infty }$See PDF-control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 836 EP - 855 VL - 18 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2011183/ DO - 10.1051/cocv/2011183 LA - en ID - COCV_2012__18_3_836_0 ER -

%0 Journal Article %A Goreac, Dan %A Serea, Oana-Silvia %T Linearization techniques for $\mathbb {L}^{\infty }$See PDF-control problems and dynamic programming principles in classical and $\mathbb {L}^{\infty }$See PDF-control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 836-855 %V 18 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2011183/ %R 10.1051/cocv/2011183 %G en %F COCV_2012__18_3_836_0

Goreac, Dan; Serea, Oana-Silvia. Linearization techniques for $\mathbb {L}^{\infty }$See PDF-control problems and dynamic programming principles in classical and $\mathbb {L}^{\infty }$See PDF-control problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 18 (2012) no. 3, pp. 836-855. doi : 10.1051/cocv/2011183. http://archive.numdam.org/articles/10.1051/cocv/2011183/

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