Linearization techniques for $\mathbb {L}^{\infty }$See PDF-control problems and dynamic programming principles in classical and $\mathbb {L}^{\infty }$See PDF-control problems

Goreac, Dan; Serea, Oana-Silvia

doi:10.1051/cocv/2011183

Geodesic

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Linearization techniques for

𝕃^{\infty}

See PDF-control problems and dynamic programming principles in classical and

𝕃^{\infty}

See PDF-control problems

Goreac, Dan ; Serea, Oana-Silvia

ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 836-855

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Résumé

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

MR Zbl

DOI : 10.1051/cocv/2011183

Classification : 34A60, 49J45, 49L20, 49L25, 93C15
Keywords: dynamic programming principle, essential supremum, hj equations, occupational measures, $\mathbb {L}^{p}$See pdf approximations

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     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},
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     publisher = {EDP-Sciences},
     volume = {18},
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     year = {2012},
     doi = {10.1051/cocv/2011183},
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     zbl = {1262.49030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011183/}
}

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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

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