A Solution to the Continuous-Time ${\\rm H}_{\\infty }$ Fixed-Interval Smoother Problem

Author

Einicke, Garry A.

Author_Institution

Commonwealth Sci. & Ind. Res. Organ. (CSIRO), Pullenvale, QLD, Australia

Volume

54

Issue

12

fYear

2009

Firstpage

2904

Lastpage

2908

Abstract

The minimum-variance fixed-interval smoother is a state-space realization of the Wiener solution generalized for time-varying problems. It involves forward and adjoint Wiener-Hopf factor inverses in which the gains are obtained by solving a Riccati equation. This technical note introduces a continuous-time H_∞ smoother having the structure of the minimum-variance version, in which the gains are obtained by solving a Riccati equation that possesses an indefinite quadratic term. It is shown that the smoother exhibits an increase in mean-square-error, the error is bounded, and the upper error bound is greater than that for the H_∞ filter.

Keywords

H^∞ control; Riccati equations; continuous time systems; mean square error methods; smoothing methods; state-space methods; time-varying systems; H_∞ filter; Riccati equation; Wiener solution; continuous-time H_∞ fixed-interval smoother problem; mean-square-error; minimum-variance fixed-interval smoother; time-varying problems; Digital filters; Estimation error; Filtering; Kalman filters; Linear matrix inequalities; Nonlinear filters; Observers; Riccati equations; Robustness; Smoothing methods; Uncertainty; ${rm H}_{infty}$ estimation; Kalman filtering; noncausal filtering; smoothing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2033857

Filename

5332246

A Solution to the Continuous-Time Fixed-Interval Smoother Problem

Einicke, Garry A.

jour

A Solution to the Continuous-Time ${\\rm H}_{\\infty }$ Fixed-Interval Smoother Problem