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Ahmet Yazıcı Abdurrahman Karamancıoğlu Refail Kasimbeyli 《Optimization and Engineering》2011,12(3):445-458
The real structured singular value (RSSV, or real μ) is a useful measure to analyze the robustness of linear systems subject to structured real parametric uncertainty, and surely
a valuable design tool for the control systems engineers. We formulate the RSSV problem as a nonlinear programming problem
and use a new computation technique, F-modified subgradient (F-MSG) algorithm, for its lower bound computation. The F-MSG
algorithm can handle a large class of nonconvex optimization problems and requires no differentiability. The RSSV computation
is a well known NP hard problem. There are several approaches that propose lower and upper bounds for the RSSV. However, with
the existing approaches, the gap between the lower and upper bounds is large for many problems so that the benefit arising
from usage of RSSV is reduced significantly. Although the F-MSG algorithm aims to solve the nonconvex programming problems
exactly, its performance depends on the quality of the standard solvers used for solving subproblems arising at each iteration
of the algorithm. In the case it does not find the optimal solution of the problem, due to its high performance, it practically
produces a very tight lower bound. Considering that the RSSV problem can be discontinuous, it is found to provide a good fit
to the problem. We also provide examples for demonstrating the validity of our approach. 相似文献
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