Fast Structured Nuclear Norm Minimization With Applications to Set Membership Systems Identification
Fast Structured Nuclear Norm Minimization With Applications to Set Membership Systems Identification
复制标题
快速结构化核规范最小化以及设置会员系统识别的应用程序
DOI：
10.1109/tac.2014.2313761
复制
发表时间：
2014
影响因子：
6.8
通讯作者：
T. Inanc
中科院分区：
文献类型：
--
作者：
M. Sznaier;Mustafa Ayazoglu;T. Inanc
集合成员身份识别寻求获得适合于在鲁棒控制框架中使用的模型。虽然在适当的假设下，这个问题是凸的，现有的方法导致高阶模型。正如我们在这篇文章中所展示的，这个困难可以通过将问题重新定义为结构化的核范数最小化来避免。为了解决这个问题，我们提出了一个计算效率高的一阶算法，只需要执行阈值和特征值分解步骤的组合。最后，由于优化只在与稳定系统的输出响应相容的序列上进行，因此保证了所识别的模型是稳定的。
Set membership identification seeks to obtain models amenable to be used in a robust control framework. While under suitable assumptions this problem is convex, existing methods lead to high order models. As we show in this note, this difficulty can be avoided by recasting the problem as a structured nuclear norm minimization. To solve this problem, we propose a computationally efficient first order algorithm that requires performing only a combination of thresholding and eigenvalue decomposition steps. Finally, since the optimization is carried out only over sequences compatible with the output responses of stable systems, the identified model is guaranteed to be stable.