Analysis of krylov subspace approximation to large-scale differential riccati equations

Abstract:

We consider a Krylov subspace approximation method for the symmetric differential Riccati equation X = AX + XAT + Q - XSX, X(0) = X0. The method we consider is based on projecting the large-scale equation onto a Krylov subspace spanned by the matrix A and the low-rank factors of X0 and Q. We prove that the method is structure preserving in the sense that it preserves two important properties of the exact flow, namely the positivity of the exact flow and also the property of monotonicity. We provide a theoretical a priori error analysis that shows superlinear convergence of the method. Moreover, we derive an a posteriori error estimate that is shown to be effective in numerical examples.

Año de publicación:

2020

Keywords:

• LQR optimal control problems
• Model order reduction
• Matrix exponential
• Exponential integrators
• Differential Riccati equations
• Krylov subspace methods
• Low-rank approximation
• Large-scale ordinary differential equations

Fuente:

scopus