# Linearization techniques for $\mathrm{See\; PDF}$-control problems and dynamic programming principles in classical and $\mathrm{See\; PDF}$-control problems

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

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

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topGoreac, 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 -

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