Numerical solution of differential Riccati equations arising in optimal control for parabolic PDEs

Abstract

AbstractThe numerical treatment of linear‐quadratic regulator problems on finite time horizons for parabolic partial differential equations requires the solution of large‐scale differential Riccati equations (DREs). Typically the coefficient matrices of the resulting DRE have a given structure (e.g. sparse, symmetric or low rank). Here we discuss numerical methods for solving DREs capable of exploiting this structure. These methods are based on a matrix‐valued implementation of the BDF methods. The crucial question of suitable stepsize and order selection strategies is also addressed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)