Robust filtering and feedforward control based on probabilistic descriptions of model errors

Abstract

A new approach to robust estimation of signals, prediction of time-series and robust feedforward control is considered. Modelling errors are parametrized by 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 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.