A fixed point-based BDF method for solving differential Riccati equations

摘要

This paper describes an approach for solving differential Riccati equations (DRE), by means of the backward differentiation formula (BDF) and resolution of the corresponding implicit equation using Newton’s method with a fixed point approach. The role and use of DRE is especially important in several applications such as optimal control, filtering, and estimation. The goodness of this new method is compared with respect to the so called Dieci method [L. Dieci, Numerical integration of the differential Riccati equation and some related issues, SIAM J. Numer. Anal. 29 (3) (1992) 781–815].