Mathematical Sciences: T+H*H Operators in Linear-Quadratic and H-Infinity Problems

本项目侧重于在 线性系统控制问题的数学理论。 这个项目的中心主题是一个操作符的形式 T + H*H，其中T是Toeplitz，H是Hankel。动机是 双重的第一，如前所述， 研究人员，线性二次型最优控制问题有一个 T + H*H算子，揭示了许多不可识别的结构 通过常规手段。第二，根据调查人员的说法， H -无穷大设计问题也涉及T + H*H 运算符，其最大特征值提供所谓的 可实现的反馈性能，一个关键参数。因此，在本发明中， 这个运算符揭示了线性 二次问题和H -无穷问题。此连接将 沿着研究其光谱和计算 方面 这项研究是在这方面进行的更大努力的一部分。 国家的理论工程师和数学家开发一个 线性控制系统的统一设计方法 对设计的鲁棒性要求。这项研究结合了 领域，如系统工程和运营商理论， 数学

This project focuses on some issues arising in the mathematical theory of control problems for linear systems. The central theme of this project is an operator of the form T + H*H where T is Toeplitz and H is Hankel. The motivation is two-fold. First, as previously shown by the principal investigator, the linear quadratic optimal control problem has a T + H*H operator that reveals a lot of structure not identifiable by conventional means. Secondly, as shown by the investigator, the H - infinity design problem alsdo involves a T + H*H operator, the largest eigenvalue of which provides the so called achievable feedback performance, a critical parameter. As such, this operator reveals a strange connection between the linear quadratic problem and H - infinity problems. This connection will be investigated along with its spectral and computational aspects. This research is part of a larger effort conducted in this country by theoretical engineers and mathematicians to develop a unified design methodology for linear control systems with robustness requirements on the design. This research combines fileds such as systems engineering and operator theory in mathematics.