Title :
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
fDate :
11/1/1997 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
