  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.
