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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Published in | IEEE transactions on automatic control Vol. 57; no. 6; pp. 1377 - 1390 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
New York, NY
IEEE
01.06.2012
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subjects | |
Online Access | Get full text |
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Summary: | 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 |