Inexact Kleinman-Newton Method for Riccati Equations

Authors

F. Feitzinger, T. Hylla, E. W. Sachs

Year

2009

Journal Paper

Algorithm

Inexact Kleinman-Newton Method

Source

SIAM Journal on Matrix Analysis and Applications

Identifiers

DOI 10.1137/070700978

Abstract¶

In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results illustrate the efficiency of this method.

Summary¶

Analyzes Kleinman-Newton iterations for algebraic Riccati equations when the internal linear solves are performed inexactly. This is important for large-scale control problems where exact Lyapunov or linear equation solves are computationally unrealistic.