Solving nonconvex optimization problems

Author

Henrion, Didier ; Lasserre, Jean-Bernard

Author_Institution

LAAS-CNRS, Toulouse, France

Volume

24

Issue

3

fYear

2004

fDate

6/1/2004 12:00:00 AM

Firstpage

72

Lastpage

83

Abstract

It is well known that most analysis and design problems in robust and nonlinear control can be formulated as global optimization problems with polynomial objective functions and constraints. The objective of this article is to show how GloptiPoly can solve challenging nonconvex optimization problems in robust nonlinear control. GloptiPoly is a general-purpose software with a user-friendly interface. First, we describe several nonconvex optimization problems arising in control system analysis and design. These problems involve multivariable polynomial objective functions and constraints. We then review the theoretical background behind GloptiPoly. Next, an example is presented to illustrate the successive linear matrix inequality relaxations and general features of the GloptiPoly software. Finally, we apply GloptiPoly to several control-related problems.

Keywords

concave programming; control engineering computing; control system analysis; control system synthesis; human computer interaction; linear matrix inequalities; nonlinear control systems; robust control; software packages; user interfaces; GloptiPoly; control system analysis; control system design; general-purpose software; nonconvex optimization problems; nonlinear control; polynomial objective functions; robust control; successive linear matrix inequality relaxations; user-friendly interface; Computational efficiency; Constraint optimization; Design optimization; Linear systems; Output feedback; Polynomials; Robust control; Robust stability; Stability analysis; Uncertainty;

fLanguage

English

Journal_Title

Control Systems, IEEE

Publisher

ieee

ISSN

1066-033X

Type

jour

DOI

10.1109/MCS.2004.1299534

Filename

1299534