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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Vydáno v:IEEE transactions on automatic control Ročník 57; číslo 6; s. 1377 - 1390
Hlavní autoři: Quoc Tran Dinh, Gumussoy, S., Michiels, W., Diehl, M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.06.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
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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Popis
Shrnutí: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2176154