Versions of inexact Kleinman-Newton methods for Riccati equations

Optimal control problems involving PDEs often lead in practice to the numerical computation of feedback laws for an optimal control. This is achieved through the solution of a Riccati equation which can be large scale, since the discretized problems are large scale and require special attention in their numerical solution. The Kleinman-Newton method is a classical way to solve an algebraic Riccati equation. We look at two versions of an extension of this method to an inexact Newton method. It can be shown that these two implementable versions of Newton's method are identical in the exact case, but differ substantially for the inexact Newton method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)