Algebraic Riccati Equations
Finding the optimal control for a continuous-time linear system with a quadratic cost function involves
solving the differential Riccati equation, which, for the case of infinite-horizon problem, simplifies
to the algebraic Riccati equation (ARE). In the literature these algebraic Riccati equations are often
solved with the Kleinman-Newton method.
In order to reduce computing time, it is mandatory that one uses iterative
solvers for the solution of the linear systems occurring at each
iteration. Therefore we analyzed inexact Newton methods in the context of
Kleinman-Newton methods and established a monotonicity
preserving convergence theory. We were also able to explain an often expierenced instability
of an alternative implementation of the Kleinman-Newton method.
Some of our main results can be found in following articels:
F. Feitzinger, T. Hylla and E.W. Sachs: Inexact Kleinman-Newton method for Riccati equations,
SIAM J. Matrix Anal. Appl., 31 (2009), pp. 272-288
T. Hylla, E. W. Sachs: Versions of inexact Kleinman-Newton
Methods for Riccati equations, PAMM Volume 7, Issue 1, (2007)
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FB 4 - Department of Mathematics |
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University of Trier |
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