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Infinite-Dimensional Sums-of-Squares for Optimal Control

Eloïse Berthier 1, 2 Justin Carpentier 3, 2 Alessandro Rudi 1, 2 Francis Bach 1, 2 
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
3 WILLOW - Models of visual object recognition and scene understanding
DI-ENS - Département d'informatique - ENS Paris, Inria de Paris
Abstract : We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial optimization to the generic case of smooth problems. Such a representation is infinite-dimensional and relies on a particular space of functions-a reproducing kernel Hilbert space-chosen to fit the structure of the control problem. After subsampling, it leads to a practical method that amounts to solving a semi-definite program. We illustrate our approach by a numerical application on a simple low-dimensional control problem.
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https://hal.archives-ouvertes.fr/hal-03377120
Contributor : Eloïse Berthier Connect in order to contact the contributor
Submitted on : Thursday, October 14, 2021 - 8:42:49 AM
Last modification on : Wednesday, June 8, 2022 - 12:50:06 PM
Long-term archiving on: : Saturday, January 15, 2022 - 6:10:28 PM

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  • HAL Id : hal-03377120, version 1
  • ARXIV : 2110.07396

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Eloïse Berthier, Justin Carpentier, Alessandro Rudi, Francis Bach. Infinite-Dimensional Sums-of-Squares for Optimal Control. 2021. ⟨hal-03377120⟩

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