Convex relaxations for quadratic distance problems

Author

Garulli, Andrea ; Masi, Alfio ; Vicino, Antonio

Author_Institution

Dipt. di Ing. dellInformazione, Univ. di Siena, Rome, Italy

fYear

2008

fDate

9-11 Dec. 2008

Firstpage

5444

Lastpage

5449

Abstract

Convex relaxations of nonconvex problems are a powerful tool for the analysis and design of control systems. An important family of nonconvex problems that are relevant to the control field is that of quadratic distance problems. In this paper, several convex relaxations are presented for quadratic distance problems which are based on the sum-of squares representation of positive polynomials. Relationships among the considered relaxations are discussed and numerical comparisons are presented, in order to highlight their degree of conservatism.

Keywords

concave programming; control system analysis; control system synthesis; convex programming; polynomials; quadratic programming; relaxation theory; control system analysis; control system design; control system synthesis; convex relaxation; nonconvex optimisation problem; positive polynomial; quadratic distance problem; sum-of square representation; Constraint optimization; Control system synthesis; Control systems; Frequency estimation; Nonlinear control systems; Nonlinear systems; Optimal control; Polynomials; Stability analysis; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2008. CDC 2008. 47th IEEE Conference on

Conference_Location

Cancun

ISSN

0191-2216

Print_ISBN

978-1-4244-3123-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2008.4739051

Filename

4739051