Duality between the discrete-time Kalman filter and LQ control law

Author

Blackmore, Perry A. ; Bitmead, Robert R.

Author_Institution

Dept. of Eng., Australian Nat. Univ., Canberra, ACT, Australia

Volume

40

Issue

8

fYear

1995

fDate

8/1/1995 12:00:00 AM

Firstpage

1442

Lastpage

1444

Abstract

In the context of linear quadratic Gaussian (LQG) controller design for single-input, single-output, discrete-time, linear, time-invariant systems, a duality is demonstrated between the Kalman filter design phase and the linear quadratic (LQ) design phase. Furthermore, an asymptotic recovery design procedure is proposed. Through specific Kalman filter design choices, the LQG open-loop transfer function is forced to approach the LQ open-loop transfer function

Keywords

Kalman filters; control system synthesis; discrete time systems; duality (mathematics); linear quadratic Gaussian control; linear systems; transfer functions; LQ control law; LQ open-loop transfer function; LQG open-loop transfer function; SISO systems; asymptotic recovery design procedure; discrete-time Kalman filter; duality; linear quadratic Gaussian controller design; single-input single-output discrete-time linear time-invariant systems; Adaptive systems; Control systems; Delay; Kalman filters; Open loop systems; Optimal control; Riccati equations; Robustness; Symmetric matrices; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.402237

Filename

402237