Exponential integrators for differential Riccati equations
摘要：Differential Riccati equations play a crucial role in optimal control and estimation theory. The solution of differential Riccati equation is usually symmetric and positive semidefinite and exhibits low-rank structure. Since the solution matrices of the differential matrix Riccati equations have these mathematical properties, the numerical methods applied should be designed to preserve those properties, this is a crucial issue in long-term simulations. In this talk, I will report our very recent results on structure preserving exponential schemes for differential matrix Riccati equations.