TY - GEN

T1 - On the least-squares approximation of structured covariances

AU - Lin, Fu

AU - Jovanović, Mihailo R.

PY - 2007/12/1

Y1 - 2007/12/1

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

UR - http://www.scopus.com/inward/record.url?scp=46449125030&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46449125030&partnerID=8YFLogxK

U2 - 10.1109/ACC.2007.4283143

DO - 10.1109/ACC.2007.4283143

M3 - Conference contribution

AN - SCOPUS:46449125030

SN - 1424409888

SN - 9781424409884

T3 - Proceedings of the American Control Conference

SP - 2648

EP - 2653

BT - Proceedings of the 2007 American Control Conference, ACC

T2 - 2007 American Control Conference, ACC

Y2 - 9 July 2007 through 13 July 2007

ER -