MINES ParisTech CAS - Centre automatique et systèmes

State-constrained Linear-Quadratic Optimal Control in light of the LQ reproducing kernel

Thursday 17th December 2020, 11am – 12am.

Pierre-Cyril Aubin, Centre Automatique et Systèmes, MINES ParisTech : https://pcaubin.github.io/

Finite-dimensional LQ problems stand at the origin of control theory. However, in presence of state constraints, they are still difficult to handle through Pontryagin's Maximum Principle. Adopting a novel viewpoint, I will 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 corresponding LQ kernel shines a new light on classical control notions, such as the Gramian of controllability. It allows tackling easily affine state constraints and provides continuous-time numerical solutions. This unveils new connections between control theory and kernel methods, an elegant field now widely used in machine learning.