Solving differential Riccati equations: A nonlinear space-time method using tensor trains

Differential Riccati equations are at the heart of many applications in control theory. They time-dependent, matrix-valued, and particular nonlinear that require special methods for their solution. Low-rank have been used heavily computing a low-rank solution every step time-discretization. We propose use an all-at-once space-time leading to large problem which we Newton–Kleinman iteration. Approximating higher-dimensional tensor form requires fewer degrees freedom operator, gives faster numerical method. Numerical experiments demonstrate storage reduction up factor 100.