Optimal reduced-order observer-estimators

摘要

A unified approach to designing reduced-order observer-estimatorsis presented. Specifically, an attempt is made to design a reduced-orderestimator satisfying an observation constraint which involves aprespecified, possibly unstable subspace of the system dynamics andwhich also yields reduced-order estimates of the remaining subspace. Theresults are obtained by merging the optimal projection approach toreduced-order estimation of D.S. Bernstein and D.C. Hyland (IEEE Trans.Autom. Control, vol.AC-30, p.583-5, 1985) with the subspace-observerresults of the authors (Proc. IEEE Conf. on Decision and Control,p.2364-6, Dec. 1988). A salient feature of this theory is the treatmentof unstable dynamics within reduced-order stable-estimation theory. Incontrast to the standard full-order estimation problem involving asingle algebraic Riccati equation, the solution to the reduced-orderobserver-estimator problem involves an algebraic system of fourequations consisting of one modified Riccati equation and three modifiedLyapunov equations coupled by two distinct oblique projections