Calculation of the structured singular value with gradient-based optimization algorithms on a Lie group of structured unitary matrices

被引：6

作者：

Dehaene, J ^{[1
]}

Yi, C ^{[1
]}

DeMoor, B ^{[1
]}

机构：

[1] DYNAM CONTROL SYST INC, DELTA, BC V4G 1H5, CANADA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 1997年 / 42卷 / 11期

关键词：

gradient-based optimization; structured singular value;

D O I：

10.1109/9.649732

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The structured singular value problem, which is a basic problem in robustness analysis and design of multivariable controllers, can be formulated as an optimization problem over the manifold of unitary matrices with a given structure. We show how geometric optimization methods, such as the steepest ascent method and the conjugate gradient method for optimization on a Riemannian manifold, lead to algorithms giving a guaranteed nontrivial lower bound for thr structured singular value.

引用

页码：1596 / 1600

页数：5

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