A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs
A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs
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不确定 LMI 可行性的概率分析中心割面法
DOI：
10.1016/j.automatica.2007.04.003
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
F. Dabbene
中科院分区：
文献类型：
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作者：
G. Calafiore;F. Dabbene
许多鲁棒控制问题可以抽象地表示为凸可行性规划，其中寻求满足形式为F <${f（x，δ）<$0，δ∈D}的一组不等式的解x。这个集合通常包含了无穷多个不等式，并且已经证明了相关的鲁棒可行性问题在一般情况下是难以数值求解的。在本文中，我们讨论了一个家庭的切割平面的方法，有效地解决了一个概率放松版本的问题。具体而言，在适当的假设下，我们表明，一个分析中心切割平面计划的基础上的概率预言返回在一个有限的和预先指定的迭代次数的解决方案x，这是可行的F的大多数成员，除了可能的子集具有任意小的概率措施。
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,δ)⩽0,δ∈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 pre-specified 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.
基于参数相关李亚普诺夫函数的鲁棒状态反馈控制器的概率设计
DOI：
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发表时间：
2003
期刊：
影响因子：
--
作者：
Takahashi;Y.;Y. Oishi
通讯作者：
Y. Oishi