An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory

被引:76
作者
Fares, B
Apkarian, P
Noll, D
机构
[1] Off Natl Etud & Rech Aerosp, CERT, Ctr Etud & Rech Toulouse, Control Syst Dept, F-31055 Toulouse, France
[2] UPS, MIP, F-31062 Toulouse, France
关键词
D O I
10.1080/00207170010010605
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We present a new approach to a class of non-convex LMI-constrained problems in robust control theory. The problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality (LMI) constraints in tandem with non-convex constraints related to rank deficiency conditions. We solve these problems using an extension of the augmented Lagrangian technique. The Lagrangian function combines a multiplier term and a penalty term governing the non-convex constraints. The LMI constraints, due to their special structure, are retained explicitly and not included in the Lagrangian. Global and fast local convergence of our approach is then obtained either by an LMI-constrained Newton type method including line search or by a trust-region strategy. The method is conveniently implemented with available semi-definite programming (SDP) interior-point solvers. We compare its performance to the well-known D - K iteration scheme in robust control. Two test problems are investigated and demonstrate the power and efficiency of our approach.
引用
收藏
页码:348 / 360
页数:13
相关论文
共 23 条
[1]  
ALIZADEH F, 1997, UNPUB J OPTIMIZATION
[2]  
[Anonymous], 1991, MU ANAL SYNTHESIS TO
[3]  
APKARIAN NP, 1999, P IEEE C DEC CONTR
[4]   Robust control via concave minimization local and global algorithms [J].
Apkarian, P ;
Tuan, HD .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2000, 45 (02) :299-305
[5]  
APKARIAN P, 1995, IEEE T AUTOMAT CONTR, V40, P1681
[6]   A CONVEX CHARACTERIZATION OF GAIN-SCHEDULED H-INFINITY CONTROLLERS [J].
APKARIAN, P ;
GAHINET, P .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (05) :853-864
[7]   SELF-SCHEDULED H-INFINITY CONTROL OF LINEAR PARAMETER-VARYING SYSTEMS - A DESIGN EXAMPLE [J].
APKARIAN, P ;
GAHINET, P ;
BECKER, G .
AUTOMATICA, 1995, 31 (09) :1251-1261
[8]   Concave programming in control theory [J].
Apkarian, P ;
Tuan, HD .
JOURNAL OF GLOBAL OPTIMIZATION, 1999, 15 (04) :343-370
[9]  
Bertsekas D.P., 2014, Constrained optimization and Lagrange multiplier methods
[10]  
Bertsekas DP, 1997, J. Oper. Res. Soc., V48, P334, DOI 10.1057/palgrave.jors.2600425