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Modeling and Analysis of Large-scale Robust Control Systems Bawd on Behavioral Approach

基于行为方法的大规模鲁棒控制系统Bawd建模与分析

基本信息

批准号：
18560431
负责人：
TAKABA Kiyotsugu
金额：
$ 1.81万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18560431/
关键词：
behavior robust control large-scale system quadratic differential form 2次微分形式システム結合

项目摘要

The behavioral approach is a new kind of system control theory that defines a dynamical system as a net of admisssible trajectories of system variables instead of an input-output mapping. Such a set of trajectories is called a behavior With the aid of JSPS Grant for Scientific Researh (C), we have investigated the Modeling and Analysis of Large-soak Robust Control Systems Based on Behavioral Approach for two years (2006-2007). Our research aimed at establishing the fundamental framework of modeling and control for large-scale complex systems by developing robust control theory from the behavioral viewpoint.The major results of this research are summarized as follows. Firstly, by studying robust stability analysis based on quadratic differential forms, we derived robust stability conditions which are generalized versions of the IQC-based stability condition of a feedback system and the robust stability via a parameter-dependent Lyapunov function. Secondly, we considered the decentralized control problem from the behavioral viewpoint, and characterized a solvability condition of the problem based on the notion of behavioral interconnections. Next we studied canonical forms of quadratic differential forms for multi-dimensional systems, and derived a new stability condition of a 2-D discrete-time system based on the quadratic difference forms. Moreover. we studied the discrete-time least square estimation problem in the behavioral framework, and developed the optimal estimation algorithm based on quadratic difference forms. Finally, for discrete event systems, we clarified the connection between the controllabilities in the behavioral framework and the supervisory control framework.

行为方法是一种新的系统控制理论，它将动态系统定义为系统变量的可容许轨迹网，而不是输入输出映射。在JSPS科学研究基金（C）的资助下，我们进行了两年（2006-2007）的基于行为方法的大浸泡鲁棒控制系统建模与分析研究。本论文的研究目的是从行为的角度发展鲁棒控制理论，建立复杂大系统建模与控制的基本框架，主要研究成果如下：首先，通过研究基于二次微分形式的鲁棒稳定性分析，我们得到了鲁棒稳定性条件，这是基于IQC的反馈系统的稳定性条件和基于参数依赖的Lyapunov函数的鲁棒稳定性的推广版本。其次，我们考虑了分散控制问题的行为的观点，并根据行为互联的概念，刻画了问题的可解性条件。其次，我们研究了多维系统二次微分形式的标准形，并基于二次微分形式导出了一个新的2-D离散系统稳定性条件。而且。在行为框架下研究了离散时间最小二乘估计问题，提出了基于二次差分形式的最优估计算法。最后，对于离散事件系统，我们澄清了行为框架和监督控制框架中的可验证性之间的联系。