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.
Accepted:
Published online:
Pierre-Cyril Aubin-Frankowski 1
@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 -
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/
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