Covariance averaging in the analysis of uncertain systems

Author

Hall, S.R.

Author_Institution

Dept. of Aeronaut. & Astronaut., MIT, Cambridge, MA

Volume

38

Issue

12

fYear

1993

fDate

12/1/1993 12:00:00 AM

Firstpage

1858

Lastpage

1862

Abstract

The effects of parametric uncertainty in stable state-space systems are analyzed by averaging the state covariance over the statistics of the uncertain parameters. For natural frequency uncertainty, this computation is related to the Fourier transform of the probability density function of the uncertain parameter. Equipartition and incoherence are illustrated for a single-mode oscillator. Averaging over a discrete uncertainty model yields the Bourret design equations while averaging over a Cauchy uncertainty distribution yields the maximum-entropy covariance equation of D.C. Hyland (1982)

Keywords

Fourier transforms; control system analysis; control system synthesis; probability; stability; state-space methods; Bourret design equations; Cauchy uncertainty distribution; Fourier transform; covariance averaging; equipartition; incoherence; maximum-entropy covariance equation; natural frequency uncertainty; parametric uncertainty; probability density function; single-mode oscillator; stable state-space systems; state covariance; Costs; Differential equations; Fourier transforms; Frequency; Probability density function; Space technology; State-space methods; Uncertain systems; Uncertainty; White noise;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.250566

Filename

250566