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

系统和控制理论是现代工程和应用数学的重要组成部分，包括与电网络，热方程和动力系统演化有关的问题。该项目开发纯数学工具，主要是复分析和泛函分析领域，以分析三个基本概念：（i）容许性，控制系统行为的方程在某种意义上是适定的;（ii）可控性，一种使系统可以通过适当的控制选择进入任何期望行为的想法精确化的方式;以及（iii）可观测性，即系统的测量产生关于系统状态的全部信息的属性。这些属性在一个一般框架中进行研究，这使得人们能够分析许多类型的演化行为。除了复分析和泛函分析的技术，它计划在上述应用的动机方向发展，它也计划追求的想法，使用数论的最新成果，以获得在这一领域的进一步信息。

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.