Higher-order relaxations for robust LMI problems with verifications for exactness
Higher-order relaxations for robust LMI problems with verifications for exactness
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针对鲁棒 LMI 问题的高阶松弛并验证准确性
DOI：
10.1109/cdc.2003.1272301
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
C. Scherer
中科院分区：
文献类型：
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作者：
C. Scherer
鲁棒半定规划问题在鲁棒控制中有着广泛的应用。对于合理的不确定性依赖，完整的块S-过程允许系统地构造松弛计算的保证界限。通常，这些松弛是保守的（导致实际和计算的最佳值之间的差距），因为它们涉及一组所谓的乘数的近似。本文的主要目的是提出一种新的序列的乘数近似，可以利用在计算中，可以证明是渐近准确的。第二个目标是提供一个数值测试，检查是否放松是准确的（从而保证没有保守性），其中扩展了最近制定的一般原则，合成问题。我们讨论了LPV合成我们的结果的实际意义，我们说明了它们的数值例子。
Robust semi-definite programming problems are know to have a wide range of applications, in particular in robust control. For rational uncertainty dependence, the full block S-procedure allows to systematically construct relaxations for the computation of guaranteed bounds. Typically these relaxations are conservative (causing a gap between actual and computed optimal values) since they involve the approximation of a set of so-called multipliers. The main purpose of this paper is to suggest a novel sequence of multiplier approximations which can be exploited in computations and which can be proved to be asymptotically exact. The second goal is to provide a numerical test for checking whether relaxations are exact (thus guaranteeing the absence of conservatism) which extends a recently formulated general principle to synthesis problems. We discuss the practical relevance of our results for LPV synthesis, and we illustrate them in terms of a numerical example.