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

通过高增益反馈进行线性和非线性系统的多时间尺度结构分配——奇异摄动方法

• 批准号: 8618953
• 负责人: Ali Saberi
• 金额: $ 7万
• 依托单位: Washington State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1990-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8618953&HistoricalAwards=false
• 关键词: Multi; Time; Scale; Structure; Assignment

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.

这项研究将研究时标结构在高增益反馈系统中的作用及其与设计针对不确定性和干扰的鲁棒性的关系。 在此基础上，探索一般动态系统时标结构分配的新概念。 此外，通过将高增益反馈方法的各种现有分析和设计放入奇异扰动系统的框架中，寻求统一和随后的推广。 通过一致地利用奇异微扰理论中体现的时间尺度分离概念，可以将给定的设计划分为子部分。 要研究的具体问题是：（1）通过二次调节器理论进行本征结构分配，（2）线性系统中本征结构和多时间尺度分配的直接方法，（3）具有内部稳定性的几乎扰动解耦，（4）保证不确定系统的稳定性，（5）具有弱测量噪声的卡尔曼滤波器，（6）多时间尺度分配和慢速和快速动态的整形 非线性系统和（7）非线性“廉价”控制问题。