On the least-squares approximation of structured covariances

Fu Lin; Mihailo R. Jovanović

doi:10.1109/ACC.2007.4283143

On the least-squares approximation of structured covariances

Fu Lin, Mihailo R. Jovanović

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

State covariances of the linear systems satisfy certain constraints imposed by the underlying dynamics. These constraints dictate a particular structure of state covariances. On the other hand, sample covariances (e.g., obtained in experiments) almost always fail to have the required structure. In view of this, it is of interest to approximate sample covariances by positive semi-definite matrices of the required structure. The structured covariance least-squares approximation problem is formulated and the Lyapunov-type matrical linear constraint is converted into an equivalent set of trace constraints. Efficient quasi Newton and generalized Newton methods capable of solving the corresponding unconstrained dual problems with the large number of variables are developed.

Original language	English (US)
Title of host publication	Proceedings of the 2007 American Control Conference, ACC
Pages	2648-2653
Number of pages	6
DOIs	https://doi.org/10.1109/ACC.2007.4283143
State	Published - Dec 1 2007
Event	2007 American Control Conference, ACC - New York, NY, United States Duration: Jul 9 2007 → Jul 13 2007

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2007 American Control Conference, ACC
Country/Territory	United States
City	New York, NY
Period	7/9/07 → 7/13/07

Keywords

Convex optimization
Least-squares approximation
Sample covariances

Publisher link

10.1109/ACC.2007.4283143

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abstract = "State covariances of the linear systems satisfy certain constraints imposed by the underlying dynamics. These constraints dictate a particular structure of state covariances. On the other hand, sample covariances (e.g., obtained in experiments) almost always fail to have the required structure. In view of this, it is of interest to approximate sample covariances by positive semi-definite matrices of the required structure. The structured covariance least-squares approximation problem is formulated and the Lyapunov-type matrical linear constraint is converted into an equivalent set of trace constraints. Efficient quasi Newton and generalized Newton methods capable of solving the corresponding unconstrained dual problems with the large number of variables are developed.",

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AU - Jovanović, Mihailo R.

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N2 - State covariances of the linear systems satisfy certain constraints imposed by the underlying dynamics. These constraints dictate a particular structure of state covariances. On the other hand, sample covariances (e.g., obtained in experiments) almost always fail to have the required structure. In view of this, it is of interest to approximate sample covariances by positive semi-definite matrices of the required structure. The structured covariance least-squares approximation problem is formulated and the Lyapunov-type matrical linear constraint is converted into an equivalent set of trace constraints. Efficient quasi Newton and generalized Newton methods capable of solving the corresponding unconstrained dual problems with the large number of variables are developed.

AB - State covariances of the linear systems satisfy certain constraints imposed by the underlying dynamics. These constraints dictate a particular structure of state covariances. On the other hand, sample covariances (e.g., obtained in experiments) almost always fail to have the required structure. In view of this, it is of interest to approximate sample covariances by positive semi-definite matrices of the required structure. The structured covariance least-squares approximation problem is formulated and the Lyapunov-type matrical linear constraint is converted into an equivalent set of trace constraints. Efficient quasi Newton and generalized Newton methods capable of solving the corresponding unconstrained dual problems with the large number of variables are developed.

KW - Convex optimization

KW - Least-squares approximation

KW - Sample covariances

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T3 - Proceedings of the American Control Conference

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BT - Proceedings of the 2007 American Control Conference, ACC

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ER -

On the least-squares approximation of structured covariances

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