DocumentCode :
2405397
Title :
Covariance averaging in the analysis of uncertain systems
Author :
Hall, Steven R. ; MacMartin, Douglas G. ; Bernstein, Dennis S.
Author_Institution :
Dept. of Aeronaut. & Astronaut., MIT, MA, USA
fYear :
1992
fDate :
1992
Firstpage :
1842
Abstract :
To analyze the effects of parametric uncertainty in state space systems, the state covariance is averaged over the statistics of the uncertain parameters. For natural frequency uncertainty, this computation is shown to be related to the Fourier transform of the probability density function of the uncertain parameter. In the case of a single mode oscillator, the average covariance exhibits both equipartition and incoherence phenomena. The analysis is carried out for several probability distributions. It is shown that 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 Hyland. For arbitrary rational distributions, the average covariance can be evaluated as the solution of a set of coupled Lyapunov equations. In addition, incoherence is demonstrated for the case of multiple modes, and the problem of robust controller synthesis with the maximum entropy design technique is considered
Keywords :
Fourier transforms; Lyapunov methods; control system analysis; control system synthesis; entropy; optimal control; probability; stability; state-space methods; stochastic systems; Bourret design equations; Cauchy uncertainty distribution; Fourier transform; H2-cost; Hyland equation; arbitrary rational distributions; coupled Lyapunov equations; covariance averaging; discrete uncertainty model; effects of parametric uncertainty; equipartition; incoherence; maximum entropy covariance equation; multiple modes; probability density function; robust controller synthesis; single mode oscillator; state covariance; state space systems; stochastic models; uncertain systems; Entropy; Equations; Fourier transforms; Frequency; Parametric statistics; Probability density function; State-space methods; Statistical analysis; Uncertain systems; Uncertainty;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 1992., Proceedings of the 31st IEEE Conference on
Conference_Location :
Tucson, AZ
Print_ISBN :
0-7803-0872-7
Type :
conf
DOI :
10.1109/CDC.1992.371111
Filename :
371111
Link To Document :
بازگشت