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

Author

Dehaene, Jeroen ; Yi, Cheng ; De Moor, Bart

Author_Institution

ESAT, Katholieke Univ., Leuven, Heverlee, Belgium

Volume

42

Issue

11

fYear

1997

fDate

11/1/1997 12:00:00 AM

Firstpage

1596

Lastpage

1600

Abstract

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 the structured singular value

Keywords

Lie groups; conjugate gradient methods; control system analysis; control system synthesis; matrix algebra; multivariable control systems; optimisation; robust control; singular value decomposition; Lie group; Riemannian manifold; conjugate gradient method; geometric optimization methods; gradient-based optimization algorithms; guaranteed nontrivial lower bound; multivariable controller design; robustness analysis; steepest ascent method; structured singular value; structured unitary matrices; unitary matrix manifold; Adaptive filters; Algorithm design and analysis; Circuits; Equations; Filtering; IIR filters; Pareto optimization; Polynomials; Signal processing algorithms; White noise;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.649732

Filename

649732