Uppsala universitet

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.

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.

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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