Calculation of the structured singular value with gradient based optimization algorithms

Author

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

Author_Institution

ESAT, Katholieke Univ., Leuven, Heverlee, Belgium

Volume

5

fYear

1995

fDate

21-23 Jun 1995

Firstpage

3034

Abstract

The structured singular value problem, which is a basic problem in robustness analysis and synthesis for control systems with structured uncertainties, can be formulated as an optimization problem over the manifold of unitary matrices with a given structure. The authors 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 with guaranteed convergence to a lower bound for the structured singular value

Keywords

control system analysis; control system synthesis; convergence; matrix algebra; optimisation; robust control; singular value decomposition; Riemannian manifold; conjugate gradient method; gradient based optimization algorithms; guaranteed convergence; robustness analysis; robustness synthesis; steepest ascent method; structured singular value; structured uncertainties; unitary matrices; Constraint optimization; Control system synthesis; Convergence; Counting circuits; Iterative algorithms; Optimization methods; Robust control; Robustness; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, Proceedings of the 1995

Conference_Location

Seattle, WA

Print_ISBN

0-7803-2445-5

Type

conf

DOI

10.1109/ACC.1995.532071

Filename

532071