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Robust Filtering and Feedforward Control based on
Probabilistic Descriptions of Model Errors
Mikael Sternad
and
Anders Ahlén
Automatica, vol 29, pp 661-679, May 1993.
© 1993 Pergamon Press.
Paper
in Pdf.
- Outline:
-
Spectral uncertainty in signal models is a problem for
model-based design of filters, predictors and smoothers.
If model errors are represented by stochastic variables,
performance robustness can be optimized by using a polynomial
equations approach.
Simple closed-form solutions exist which minimize quadratic criteria,
averaged with respect to the model error distribution.
- Abstract:
-
A new approach to robust estimation of signals, prediction of
time-series and robust feedforward control is considered.
Signal and system parameter deviations are represented
as random variables, with known covariances.
A robust design is obtained
by minimizing the squared estimation error, averaged both
with respect to model errors and the noise.
A polynomial equations approach, based on
averaged spectral factorizations and averaged Diophantine equations,
is derived. Mild solvability conditions guarantee the
existence of stable optimal filters and feedforward regulators.
The robust design turns out to be no more
complicated than the design of an ordinary Wiener filter or
LQG regulator.
The proposed approach avoids two drawbacks of
robust minimax design.
First, probabilistic
descriptions of model uncertainties may have
soft bounds .
These are more readily obtainable
in a noisy environment than the hard bounds required for
minimax design. Furthermore, not only
the range of uncertainties, but also their likelihood is
taken into account;
common model deviations will
have a greater impact on an estimator design than do
very rare ``worst cases''.
The conservativeness is thus reduced.
- Related publications:
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Paper
in IEEE Trans AC 1995, which generalizes to the multivariable
case.
PhD Thesis
by Kenth Öhrn, May 1996, with more details, examples
and generalizations.
PhD Thesis by Erik Lindskog,
treating robustness in decision feedback equalizers.
State-space design
and comparison to minimax H-2, European Control Conf. 1995.
Paper
in IEEE Trans. SP 1991 on the polynomial approach to
(nominal) Wiener filter design.
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Research
on polynomial methods
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Main
entry in list of publications
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