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

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络，而不是输入-输出映射。在JSPS科学研究基金(C)的帮助下，我们对基于行为方法的大型鲁棒控制系统的建模和分析进行了两年（2006-2007）的研究。我们的研究旨在从行为的角度发展鲁棒控制理论，建立大型复杂系统建模和控制的基本框架。本研究的主要成果总结如下：首先，通过研究基于二次微分形式的鲁棒稳定性分析，导出了反馈系统基于iqc的鲁棒稳定性条件的广义化版本和参数相关Lyapunov函数的鲁棒稳定性。其次，从行为的角度考虑分散控制问题，并基于行为互联的概念刻画了问题的可解性条件。其次，研究了多维系统的二次差分形式的标准形式，并基于二次差分形式导出了二维离散系统的一个新的稳定性条件。此外。研究了行为框架下的离散最小二乘估计问题，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可控性之间的联系。

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.