Spaces of analytic functions, applied to well-posedness and controllability of linear systems

系统与控制理论是现代工程和应用数学的一个重要组成部分，它包括，例如，与电力网络、热方程和动力系统演化有关的问题。这个项目开发了纯数学的工具，主要是复杂分析和泛函分析领域的工具，以分析三个基本概念：(I)容许性，控制系统行为的方程在一定意义上是适定的；(Ii)可控性，一种精确的想法，即通过适当的控制选择，系统可以被引导到任何期望的行为；以及(Iii)可观测性，系统的测量产生关于系统状态的全部信息。这些属性在一个一般的框架中研究，这使得一个人能够分析许多类型的演化行为。除了复杂分析和泛函分析的技术外，还计划在上述应用的推动下朝着方向发展，还计划利用数论的最新结果来获得这一领域的更多信息。

The theory of systems and control is a key component of modern engineering and applied mathematics, and includes, for example, problems related to electrical networks, the heat equation, and the evolution of dynamical systems. This project develops tools from pure mathematics, mostly the areas of complex analysis and functional analysis, in order to analyse three fundamental notions:(i) admissibility, needed for the equations governing the system's behaviour to be well-posed in a certain sense;(ii) controllability, a way of making precise the idea that a system can be steered into any desired behaviour by a suitable choice of control; and(iii) observability, the property that measurements of the system yield full information about the state of the system.These properties are studied in a general framework, which enables one to analyse many types of evolving behaviour. In addition to the techniques in complex analysis and functional analysis, which it is planned to develop in directions motivated by the applications above, it is also planned to pursue the idea of using recent results in number theory to obtain further information in this area.