Linearization techniques for 𝕃 ∞ See PDF-control problems and dynamic programming principles in classical and 𝕃 ∞ See PDF-control problems

Dan Goreac; Oana-Silvia Serea

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 3, page 836-855
  • ISSN: 1292-8119

Abstract

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The aim of the paper is to provide a linearization approach to the 𝕃 ∞ 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 𝕃 p See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating 𝕃 ∞ See PDF problems in continuous and lower semicontinuous setting.

How to cite

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Goreac, Dan, and 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 18.3 (2012): 836-855. <http://eudml.org/doc/272836>.

@article{Goreac2012,
abstract = {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.},
author = {Goreac, Dan, Serea, Oana-Silvia},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {dynamic programming principle; essential supremum; hj equations; occupational measures; $\mathbb \{L\}^\{p\}$See pdf approximations; HJ equations; -approximations},
language = {eng},
number = {3},
pages = {836-855},
publisher = {EDP-Sciences},
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},
url = {http://eudml.org/doc/272836},
volume = {18},
year = {2012},
}

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
PB - EDP-Sciences
VL - 18
IS - 3
SP - 836
EP - 855
AB - 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.
LA - eng
KW - dynamic programming principle; essential supremum; hj equations; occupational measures; $\mathbb {L}^{p}$See pdf approximations; HJ equations; -approximations
UR - http://eudml.org/doc/272836
ER -

References

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