Comptes Rendus
Théorie du contrôle
Interpreting the dual Riccati equation through the LQ reproducing kernel
Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 199-204.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.174

Pierre-Cyril Aubin-Frankowski 1

1 École des Ponts ParisTech and CAS, MINES ParisTech, PSL Research University, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2021__359_2_199_0,
     author = {Pierre-Cyril Aubin-Frankowski},
     title = {Interpreting the dual {Riccati} equation through the {LQ} reproducing kernel},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {199--204},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {2},
     year = {2021},
     doi = {10.5802/crmath.174},
     language = {en},
}
TY  - JOUR
AU  - Pierre-Cyril Aubin-Frankowski
TI  - Interpreting the dual Riccati equation through the LQ reproducing kernel
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 199
EP  - 204
VL  - 359
IS  - 2
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.174
LA  - en
ID  - CRMATH_2021__359_2_199_0
ER  - 
%0 Journal Article
%A Pierre-Cyril Aubin-Frankowski
%T Interpreting the dual Riccati equation through the LQ reproducing kernel
%J Comptes Rendus. Mathématique
%D 2021
%P 199-204
%V 359
%N 2
%I Académie des sciences, Paris
%R 10.5802/crmath.174
%G en
%F CRMATH_2021__359_2_199_0
Pierre-Cyril Aubin-Frankowski. Interpreting the dual Riccati equation through the LQ reproducing kernel. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 199-204. doi : 10.5802/crmath.174. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.174/

[1] Pierre-Cyril Aubin-Frankowski Linearly-constrained Linear Quadratic Regulator from the viewpoint of kernel methods (2020) (https://arxiv.org/abs/2011.02196)

[2] Viorel Barbu; Giuseppe Da Prato A representation formula for the solutions to operator Riccati equation, Differ. Integral Equ., Volume 5 (1992) no. 4, pp. 821-829 | MR | Zbl

[3] Alain Bensoussan; Giuseppe Da Prato; Michel C. Delfour; Sanjoy K. Mitter Representation and Control of Infinite Dimensional Systems, Birkhäuser, 2007 | DOI | Zbl

[4] David Luenberger Optimization by vector space methods, John Wiley & Sons, 1968

[5] Mario Micheli; Joan A. Glaunès Matrix-valued kernels for shape deformation analysis, Geometry, Imaging and Computing, Volume 1 (2014) no. 1, pp. 57-139 | DOI | MR | Zbl

[6] Saburou Saitoh; Yoshihiro Sawano Theory of Reproducing Kernels and Applications, Developments in Mathematics, 44, Springer, 2016 | MR | Zbl

[7] Bernhard Schölkopf; J. Smola Learning with kernels : support vector machines, regularization, optimization, and beyond, MIT Press, 2002

Cité par Sources :

Commentaires - Politique