广义系统下含不稳定和非正则加权函数的奇异控制问题

项目名称： 广义系统下含不稳定和非正则加权函数的奇异控制问题

项目编号： No.61203130

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： 冯宇

作者单位： 浙江工业大学

项目金额： 23万元

中文摘要： 标准H2和H无穷控制于上世纪八十年代末达到一个相对成熟的发展程度。但对于奇异问题，即系统含有有限虚轴零点或无穷远零点，标准方法无法解决。同时，在实际应用中往往需要使用输入输出加权函数，达到模拟环境变量或保证控制精度的目的。而此类加权函数通常是不稳定及不可镇定（或不检测）的。由于这些加权函数的存在，整体系统变得不可被内镇定。在标准控制理论框架下，此类问题无法解决。本项目将在广义系统环境下，来研究含有不稳定和非正则加权函数的奇异H2和H无穷控制问题。通过对标准广义Riccati法的推广和使用准容许法，将含有加权函数的奇异控制问题转化为一个降阶的标准控制问题，并给出满足条件控制器的参数化形式。同时，系统本身有限虚轴零点、无穷远零点和加权函数对控制器的影响，以及现有LMI法在处理奇异问题时的保守性也将被深入研究。这一项目的成功实施，将对控制理论的发展产生积极的影响，具有重要的理论意义和应用价值。

中文关键词： 鲁棒控制；不稳定和非正则加权函数；广义系统；H2；H无穷

英文摘要： The standard H2 and H infinity control theory reached a fairly mature state in the late 1980s. However, the singular problem, that is the plant has zeros on the imaginary axis including infinity, cannot be handled by the standard control theory. Moreover, in many practical contexts, it is often desirable to take unstable, even nonproper, weighting filters in order to define the environment variables or to meet the design specifications. These choices generally result in a nonstandard design problem for plants having unstabilizable (undetectable) dynamics due to the weights involved. This project is concerned with the singular H2 and H infinity control for descriptor systems with unstable and nonproper weights. By extending the standard generalized Riccati-based approach and employing the quasi-admissibility method, the singular problems will be transformed into conventional reduced-order control problems, and the parameterization of all controllers will be deduced. In addition, the impacts of the zeros on the imaginary axis including infinity and the used weighting filters on the resulting controllers will be detailed; while conservatism of the existing LMI-based approaches for dealing with the singular problems will also be investigated. The success of this project has a significant impact on development of con

英文关键词： robust control；unstable and nonproper weights；descriptor systems；H2；H infinity