The aim of the paper is to provide a linearization approach to the 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 See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating See PDF problems in continuous and lower semicontinuous setting.
Mots-clés : 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
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%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2012
%P 836-855
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%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv/2011183/
%R 10.1051/cocv/2011183
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%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, Tome 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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