Global optimization for the biaffine matrix inequality problem

被引：78

作者：

Goh, KC ^{[1
]}

Safonov, MG ^{[1
]}

Papavassilopoulos, GP ^{[1
]}

机构：

[1] UNIV SO CALIF, LOS ANGELES, CA 90089 USA

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 1995年 / 7卷 / 04期

关键词：

branch and bound; bilinear matrix inequalities; linear matrix inequalities; robust control;

D O I：

10.1007/BF01099648

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

It has recently been shown that an extremely wide array of robust controller design problems may be reduced to the problem of finding a feasible point under a Biaffine Matrix Inequality (BMI) constraint. The BMI feasibility problem is the bilinear version of the Linear (Affine) Matrix Inequality (LMI) feasibility problem, and may also be viewed as a bilinear extension to the Semidefinite Programming (SDP) problem, The BMI problem may be approached as a biconvex global optimization problem of minimizing the maximum eigenvalue of a biaffine combination of symmetric matrices. This paper presents a branch and bound global optimization algorithm for the BMI. A simple numerical example is included, The robust control problem, i.e., the synthesis of a controller for a dynamic physical system which guarantees stability and performance in the face of significant modelling error and worst-case disturbance inputs, is frequently encountered in a variety of complex engineering applications including the design of aircraft, satellites, chemical plants, and other precision positioning and tracking systems.

引用

页码：365 / 380

页数：16

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