Iterative Refinement Procedure for Solutions to Algebraic Riccati Equations

摘要

This paper presents an algorithm for the iterative refinement of matrix solutions for the algebraic Riccati equation in both the continuous and discrete-time cases. It is based on Newton's method for root-finding and extended using the Fréchet derivative framework. The improvement brought by the paper is in considering the complete structure of the algebraic Riccati equations, which typically consider the input-state dependency matrix to be zero. This approach is reasonable for computing linear quadratic regulators and estimators, but must be treated in the field of Robust Control, as the algebraic Riccati equations which arise in H2/H∞ synthesis methods have the complete structure. Numerical results are also presented and it is shown that the method brings important improvements, in particular for ill-conditioned problems, i.e. when the system controllability is ill-conditioned.