一类噪声有界变量带误差模型的频域鲁棒辨识方法研究

项目名称： 一类噪声有界变量带误差模型的频域鲁棒辨识方法研究

项目编号： No.61203119

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 耿立辉

作者单位： 天津职业技术师范大学

项目金额： 25万元

中文摘要： 变量带误差（EIV: Errors-In-Variables）模型的辨识是近年系统辨识领域的研究热点。由于该模型同时考虑输入和输出变量受扰动噪声的污染，其应用领域更加广泛。但是，因受噪声特性和模型结构的限制，EIV模型的辨识难度很大。本课题拟针对一类有界噪声，研究采用表征为正规右图符号（NRGS: Normalized Right Graph Symbol，或称正规右互质因子）的名义模型及其最坏情况误差界描述模型集合的频域鲁棒辨识方法。在考虑系统导数界有限或无限情况下，以v-gap度量定义先验噪声集合，通过预实验估计先验系统集合和先验噪声集合，利用优化方法获得名义NRGS模型，并对该名义模型的最坏情况误差界进行量化，以获得具有较少保守性的NRGS加法扰动模型集合。课题除了利用数值仿真和机器人控制实验系统验证所研究的辨识方法的有效性外，还将在理论上严格证明辨识方法的收敛性。

中文关键词： 变量带误差；鲁棒辨识方法；有界噪声；扰动模型集；频域

英文摘要： Identification of errors-in-variables (EIV) models has been an eye-catching focus in the area of system identification in recent years. Since this model considers the input and output noise simultaneously, its application is rather widespread. Nevertheless, it is difficult to estimate an EIV model due to the restriction from the noise property and model structure. As for a class of bounded noise, this project focuses on frequency-domain robust identification methods, in which a model set is described by a nominal model characterized by a normalized right graph symbol (NRGS, also normalized right coprime factors) and its worst-case error bound. In the case of a finite or infinite derivative bound of the underlying system, the v-gap metric is used to define an a priori noise set, and the a priori system and noise sets can then be estimated from some pre-experiments. On the basis of the optimized nominal NRGS model and its worst-case error bound, an additive perturbed NRGS model set with less conservativeness can thus be obtained. In addition to numerical simulations and applications to a robotic control system for effectiveness verification of the proposed methods, their robust convergent properties will also be rigorously proved.

英文关键词： errors-in-variables；robust identification method；bounded noise；perturbed model set；frequency domain