A probabilistic analytic center cutting plane method for feasibility of uncertain LMls

被引:33
|
作者
Calafiore, Giuseppe C. [1 ]
Dabbene, Fabrizio [2 ]
机构
[1] Politecn Torino, Dipartimento Automat & Informat, I-10129 Turin, Italy
[2] Politecn Torino, CNR, IEIIT, I-10129 Turin, Italy
关键词
randomized algorithms; uncertain linear matrix inequalities; robust control;
D O I
10.1016/j.automatica.2007.04.003
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Many robust control problems can be formulated in abstract form as convex feasibility programs, where one seeks a solution x that satisfies a set of inequalities of the form F = {f(x, delta) <= 0, delta is an element of D}. This set typically contains an infinite and uncountable number of inequalities, and it has been proved that the related robust feasibility problem is numerically hard to solve in general. In this paper, we discuss a family of cutting plane methods that solve efficiently a probabilistically relaxed version of the problem. Specifically, under suitable hypotheses, we show that an Analytic Center Cutting Plane scheme based on a probabilistic oracle returns in a finite and prespecified number of iterations a solution x which is feasible for most of the members of F, except possibly for a subset having arbitrarily small probability measure. (c) 2007 Elsevier Ltd. All rights reserved.
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页码:2022 / 2033
页数:12
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