New Methods in Modeling and Control of Dynamical Systems

这是对建模的某些方面的研究， 动力系统的控制 尤其是 线性系统建模与控制的综合方法 动力系统将根据 图的概念。 图的概念 动力系统和差距度量的概念是 系统理论中的重要新思想。 差距度量 是一个适合使用的系统之间距离的概念 在鲁棒稳定和控制的背景下。 线性动力系统模型的逼近 可以使用差距度量来完成。 这是 动机是需要综合控制器， “低”阶模型。 建模的描述 误差自然以不确定性的形式出现， 一个给定系统的图--图是所有 系统的有界输入输出对。 第一 其中一部分研究就是这种建模理论。 在研究的第二部分， 使用自相关估计的建模 将开发给定信号的功能。 在 特别是，测量噪声输入输出数据的 未知的线性系统也可以纳入这个框架。 一种递归谱估计方法 提出了自相关（协方差）数据。 差距 度量将被用来获得先验界 谱估计和不确定性的估计 在所寻求的模型的图中。 研究的第三部分将继续进行 关于采取新办法， 谱分解 这是基于一系列的 在给定的线性系统的图形上的变换。 该技术基于迭代方案， 有可能实现快速高效的 谱分解和递归算法 过滤

This is research on certain aspects of modeling and control of dynamical systems. In particular, an integrated approach to modeling and control of linear dynamical systems will be developed based on the notion of a graph. The notion of a graph of a dynamical system and the notion of the gap metric are important new ideas in systems theory. The gap metric is a notion of distance between systems suitable for use in the context of robust stabilization and control. Approximation of models of linear dynamical systems can be done with use of the gap metric. This is motivated by the need to synthesize controllers using "low" order models. The description of the modeling error appears naturally in the form of uncertainty in the graph of a given system -- graph being the set of all bounded input-output pairs of the system. The first part of the research will be on such modeling theory. In the second part of the research, a framework of modeling which uses estimates of the autocorrelation function of a given signal will be developed. In particular, measuring noisy input-output data of an unknown linear system can be cast into this framework. An approach to recursive spectral estimation based on autocorrelation (covariance) data is proposed. The gap metric will be used to obtain a-priori bounds on spectral estimates and on estimates of the uncertainty in the graph of the sought model. The third part of the research will be to continue the development of recent results on a new approach to spectral factorization. This is based on a sequence of transformations on the graph of a given linear system. The technique is based on an iterative scheme and holds the potential of leading to fast and efficient algorithms for spectral factorization and recursive filtering.