Mathematical Sciences: Operator and Systems Theory

本项目将研究H ∞控制理论。 的 要强调的主题是线性时不变有限- 维植物，Wiener-Hopf分解和插值 对于有理矩阵函数，分布参数系统，以及 非线性系统的H ∞优化。 莫尔斯理论， 算子和函数理论预计将发挥核心作用。 需要研究的问题是 控制工程系统。 该项目包括非线性 已知的窄带频率理论 并不适用。 计算机代码将在成功后开发 对基本数学理论的理解。

This project will study H-infinity control theory. The topics to be emphasized are linear time-invariant finite- dimensional plants, Wiener-Hopf factorization and interpolation for rational matrix functions, distributed parameter systems, and H-infinity optimization for nonlinear systems. Morse theory, operator and function theory are expected to play a central role. The problems to be studied are motivated by the need of controlling engineering systems. This project includes nonlinear cases where the known theory for a narrow band of frequencies does not apply. Computer codes will be developed upon successful understanding of the underlying mathematical theory.