The Caratheodory-Fejer problem and H/sub /spl infin// identification: a time domain approach
The Caratheodory-Fejer problem and H/sub /spl infin// identification: a time domain approach
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Caratheodory-Fejer 问题和 H/sub /spl infin// 识别：时域方法
DOI：
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发表时间：
1993
期刊：
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通讯作者：
C. Nett
中科院分区：
文献类型：
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作者：
Jie Chen;C. Nett
解决了最坏情况下的面向鲁棒控制的辨识问题。这个问题是H/SUB/SPL/INFIN//辨识问题的一般框架中的一个变体，已有几位作者研究过。在这个问题中，可用的先验信息由对象相对稳定性的下界、与对象相关的某一增益的上界和噪声水平的上界组成。假设待识别的植物位于H/SUB/SPL inin//空间中的某个子集中。可用的实验信息由一个损坏的有限输出时间序列组成，该时间序列是响应于已知的非零输入而获得的，但在其他方面是任意的。目标是从给定的先验和实验信息中识别不确定模型，该模型包括以H/SUB/SPL//范数表示的标称对象模型和以H/SUB/SPL//范数测量的建模误差的界。给出了一个辨识误差和辨识误差的几个显式上下界。该算法属于插值型算法，在减小辨识误差方面具有理想的最优性。该算法可以通过用标准的凸规划方法求解推广的Caratheodory-Fejer问题而得到。这些误差界不仅给出了建模误差的显式估计，而且还被用来建立所提出的辨识算法的收敛性质。
Addresses a worst-case, robust control oriented identification problem. This problem is a variant in the general framework of H/sub /spl infin// identification problems which have been studied by several authors. In this problem the available a priori information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The plant to be identified is assumed to lie in a certain subset in the space of H/sub /spl infin//. The available experimental information consists of a corrupt finite output time series obtained in response to a known nonzero but otherwise arbitrary input. The objective is to identify from the given a priori and experimental information an uncertain model which includes a nominal plant model in H/sub /spl infin// and a bound on the modeling error measured in H/sub /spl infin// norm. The authors present both an identification error and several explicit lower and upper bounds on the identification error. The proposed algorithm is in the class of interpolatory algorithms which are known to posses desirable optimality properties in reducing the identification error. This algorithm may be obtained by solving an extended Caratheodory-Fejer problem via standard convex programming methods. The error bounds not only provide explicit estimates on the modeling error, but also are used to establish the convergence properties of the proposed identification algorithm.<<ETX>>