Uppsala universitet

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.

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.

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:
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.

| Research on polynomial methods | Main entry in list of publications |
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