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A Probabilistic Approach to Multivariable Robust Filtering
and Open-loop Control
Kenth Öhrn
,
Anders Ahlén
and
Mikael Sternad
IEEE Transactions on Automatic Control ,
vol 40, pp 405-418, March 1995.
© 1995 IEEE.
Also: Internal Report UPTEC 93008R, Dept. of Technology,
Uppsala University.
Paper In Pdf 1168K.
- Outline:
-
The performance of Wiener filters is degraded by the presence of
model errors. The paper
develops a method for robust desing
of multisignal estimators. It is based on probabilistic descriptions
of the uncertainty and on the minimization of averaged
mean square error criteria.
- Abstract:
-
A new approach to robust filtering, prediction and smoothing of
discrete-time signal vectors is presented.
Linear time-invariant filters are designed to be insensitive
to spectral uncertainty in signal models.
The goal is to obtain a simple design method,
leading to filters which are not overly conservative.
Modelling errors are described by sets of models, parameterized
by random variables with known covariances.
These covariances could either be estimated from data, or be used
as robustness ``tuning knobs".
A robust design is obtained by minimizing the H-2 norm
or, equivalently, the mean square estimation error, averaged
with respect to the assumed model errors.
A polynomial solution, based on an averaged spectral
factorization and a unilateral Diophantine equation, is derived.
The robust estimator is referred to as a cautious Wiener
filter. It turns out to be only slightly more complicated to
design than an ordinary Wiener filter.
The methodology can be applied to any open loop filtering
or control problem.
In particular, we illustrate this for the design of robust
multivariable feedforward regulators, decoupling and model
matching filters.
- Related publications:
-
PhD Thesis
by Kenth Öhrn, May 1996, with details, examples and
generalizations.
SISO case
and uncertainty modelling, as described in Automatica 1993.
Book chapter
(Springer, 1996), outlining the nominal and the robust design.
Robust decision feedback equalizers,
IEEE ICASSP'93.
PhD Thesis by Erik Lindskog,
treating robustness in decision feedback equalizers.
State-space design
and comparison to minimax H-2, European Control Conf. 1995.
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