Volume 18, Number 3, July-September 2012
|Page(s)||836 - 855|
|Published online||17 August 2011|
Linearization techniques for -control problems and dynamic programming principles in classical and -control problems
UniversitéParis-Est Marne-la-Vallée, LAMA, UMR8050,
5, boulevard Descartes, Cité Descartes,
2 Université de Perpignan, LAMPS, 52, av. Paul Alduy, 66860 Perpignan and École Polytechnique, CMAP, Route de Saclay, 91128 Palaiseau Cedex, France
Received: 9 February 2011
Revised: 14 May 2011
The aim of the paper is to provide a linearization approach to the -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 approach and the associated linear formulations. This seems to be the most appropriate tool for treating problems in continuous and lower semicontinuous setting.
Mathematics Subject Classification: 34A60 / 49J45 / 49L20 / 49L25 / 93C15
Key words: Dynamic programming principle / essential supremum / HJ equations / occupational measures / 𝕃p approximations
© EDP Sciences, SMAI, 2011
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