https://hal-enpc.archives-ouvertes.fr/hal-03090198Aubin-Frankowski, Pierre-CyrilPierre-CyrilAubin-FrankowskiENPC - École des Ponts ParisTechCAS - Centre Automatique et Systèmes - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettresInterpreting the dual Riccati equation through the LQ reproducing kernelHAL CCSD2020[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Aubin-Frankowski, Pierre-Cyril2020-12-29 13:25:032022-10-22 05:15:362021-01-05 14:21:20enJournal articlesapplication/pdf1In 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.