Multi-Time-Scale Structure Assignment in Linear and Nonlinear Systems by High-Gain Feedback -- Singular Perturbation Approach

这项研究将考察时间尺度结构在高增益反馈系统中的作用及其与设计在不确定和干扰方面的稳健性的关系。在此基础上，提出了一般动态系统时间尺度结构配置的新概念。此外，通过将各种已有的高增益反馈方法的分析和设计放入奇异摄动系统的框架中，寻求它们的统一和相应的推广。通过一致地利用奇异摄动理论中体现的时间尺度分离概念，使得将给定设计划分为子部分变得容易。要研究的具体问题是：(1)基于二次调节器理论的特征结构配置，(2)线性系统的特征结构和多时间尺度配置的直接方法，(3)几乎干扰与内部稳定性的解耦，(4)不确定系统的保证稳定性，(5)具有弱测量噪声的卡尔曼滤波，(6)非线性系统中慢动态和快动态的多时间尺度分配和整形；(7)非线性“廉价”控制问题。

This research will examine the role of time-scale structure in high-gain feedback systems and its relation to robustness of a design with respect to uncertainties and disturbances. Based on this, a novel concept of time-scale structure assignment for general dynamic systems is to be explored. Furthermore, unification and consequent generalization of various exisiting analysis and design of high-gain feedback methods is sought by casting them into the framework of singularly perturbed systems. Partitioning of a given design into subparts is facilitated through consistent exploitation of time-scale separation concepts embodied in singular perturbation theory. The specific problems which are to be examined are: (1) Eigenstructure assignment via quadratic regulator theory , (2) Direct methods of eigenstructure and multiple time-scale assignment in linear systems, (3) Almost disturbance decoupling with internal stability, (4) Guaranteed stability of uncertain systems, (5) Kalman filter with weak measurement noise, (6) Multiple time-scale assignment and shaping of slow and fast dynamics in nonlinear systems and (7) Nonlinear "cheap" control problems.