Author(s) :
Peter Benner
,
Ralph Byers
,
Volker Mehrmann
,
Hongguo Xu
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 06-2004
MSC 2000
- 93B40 Computational methods
-
93B36 $^\infty$-control
Abstract :
We present numerical methods for the
solution of the optimal $H_{\infty}$
control problem.
In particular, we investigate the iterative
part often called the $\gamma$-iteration.
We derive a method with better robustness in the presence of
rounding errors than other existing methods.
It remains robust in the presence of rounding errors
even as $\gamma$ approaches its optimal value.
For the computation of a suboptimal controller,
we avoid solving algebraic Riccati equations
with their problematic matrix inverses and matrix products
by adapting recently suggested
methods for the computation of deflating subspaces of
skew-Hamiltonian/Hamiltonian pencils.
These methods are applicable even if the pencil has
eigenvalues on the imaginary axis.
We compare the new method with older methods and present
several examples.
Keywords :
$H_\infty$ control, algebraic Riccati equation, $CS$ decomposition,Lagrangian subspaces, skew-Hamiltonian/Hamiltonian pencil