Combining Convex-Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback

A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is l...

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Veröffentlicht in:	IEEE transactions on automatic control Jg. 57; H. 6; S. 1377 - 1390
Hauptverfasser:	Quoc Tran Dinh, Gumussoy, S., Michiels, W., Diehl, M.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.06.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Applied sciences Benchmarking Bilinear matrix inequality (BMI) Bismaleimides Computer science; control theory; systems Control system analysis Control system synthesis Control theory. Systems Convergence Convex functions convex-concave decomposition Decomposition Exact sciences and technology Inequalities Linear matrix inequalities linear time-invariant system Mapping Matrix decomposition Optimization Output feedback Programming semidefinite programming static feedback controller design Vectors linear time-invariant system Feedback regulation Control synthesis Semi definite programming Matrix inequality Bilinear form Convex programming Optimization convex―concave decomposition semidefinite programming Linear time invariant system static feedback controller design Bilinear matrix inequality (BMI) Linear matrix inequality Convex function Bilinear transform Output feedback Linearization
ISSN:	0018-9286, 1558-2523
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Abstract	A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem. Applications to various output feedback controller synthesis problems are presented. In these applications, the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from the COMPl e ib library.
AbstractList	A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem. Applications to various output feedback controller synthesis problems are presented. In these applications, the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from the rm COMPl rm e rm ib library. A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem. Applications to various output feedback controller synthesis problems are presented. In these applications, the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from the COMPl e ib library. A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem. Applications to various output feedback controller synthesis problems are presented. In these applications, the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from the [Formula Omitted] library.
Author	Quoc Tran Dinh Michiels, W. Diehl, M. Gumussoy, S.
Author_xml	– sequence: 1 surname: Quoc Tran Dinh fullname: Quoc Tran Dinh email: quoc.trandinh@esat.kuleuven.be organization: Fac. of Math.-Mech.-Inf., Hanoi Univ. of Sci., Hanoi, Vietnam – sequence: 2 givenname: S. surname: Gumussoy fullname: Gumussoy, S. email: suat.gumussoy@mathworks.com organization: Dept. of Comput. Sci., Katholieke Univ., Leuven, Belgium – sequence: 3 givenname: W. surname: Michiels fullname: Michiels, W. email: wim.michiels@cs.kuleuven.be organization: Dept. of Comput. Sci., Katholieke Univ. Leuven, Leuven, Belgium – sequence: 4 givenname: M. surname: Diehl fullname: Diehl, M. email: moritz.diehl@esat.kuleuven.be organization: Dept. of Electr. Eng., Katholieke Univ. Leuven, Leuven, Belgium
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Keywords	linear time-invariant system Feedback regulation Control synthesis Semi definite programming Matrix inequality Bilinear form Convex programming Optimization convex―concave decomposition semidefinite programming Linear time invariant system static feedback controller design Bilinear matrix inequality (BMI) Linear matrix inequality Convex function Bilinear transform Output feedback Linearization
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SubjectTerms	Algorithms Applied sciences Benchmarking Bilinear matrix inequality (BMI) Bismaleimides Computer science; control theory; systems Control system analysis Control system synthesis Control theory. Systems Convergence Convex functions convex-concave decomposition Decomposition Exact sciences and technology Inequalities Linear matrix inequalities linear time-invariant system Mapping Matrix decomposition Optimization Output feedback Programming semidefinite programming static feedback controller design Vectors
Title	Combining Convex-Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback
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