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

How to cite

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Goreac, Dan, and Serea, Oana-Silvia. "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 18.3 (2012): 836-855. <http://eudml.org/doc/244349>.

@article{Goreac2012,
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. },
author = {Goreac, Dan, Serea, Oana-Silvia},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Dynamic programming principle; essential supremum; HJ equations; occupational measures; $\mathbb\{L\}^\{p\}$ approximations; dynamic programming principle; -approximations},
language = {eng},
month = {11},
number = {3},
pages = {836-855},
publisher = {EDP Sciences},
title = {Linearization techniques for $\mathbb\{L\}^\{\infty\}$-control problems and dynamic programming principles in classical and $\mathbb\{L\}^\{\infty\}$-control problems},
url = {http://eudml.org/doc/244349},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Goreac, Dan
AU - Serea, Oana-Silvia
TI - Linearization techniques for $\mathbb{L}^{\infty}$-control problems and dynamic programming principles in classical and $\mathbb{L}^{\infty}$-control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/11//
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 $\mathbb{L}^{\infty}$-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.
LA - eng
KW - Dynamic programming principle; essential supremum; HJ equations; occupational measures; $\mathbb{L}^{p}$ approximations; dynamic programming principle; -approximations
UR - http://eudml.org/doc/244349
ER -

References

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