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Interpreting the dual Riccati equation through the LQ reproducing kernel

Abstract : In this study, we provide an interpretation of the dual differential Riccati equation of Linear-Quadratic (LQ) optimal control problems. Adopting a novel viewpoint, we show that LQ optimal control can be seen as a regression problem over the space of controlled trajectories, and that the latter has a very natural structure as a reproducing kernel Hilbert space (RKHS). The dual Riccati equation then describes the evolution of the values of the LQ reproducing kernel when the initial time changes. This unveils new connections between control theory and kernel methods, a field widely used in machine learning.
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https://hal-enpc.archives-ouvertes.fr/hal-03090198
Contributor : Pierre-Cyril Aubin-Frankowski <>
Submitted on : Tuesday, December 29, 2020 - 1:25:03 PM
Last modification on : Thursday, January 7, 2021 - 3:07:24 AM
Long-term archiving on: : Tuesday, March 30, 2021 - 7:08:51 PM

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  • HAL Id : hal-03090198, version 1

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Pierre-Cyril Aubin-Frankowski. Interpreting the dual Riccati equation through the LQ reproducing kernel. Comptes Rendus Mathématique, Elsevier Masson, inPress. ⟨hal-03090198⟩

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