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

解析函数空间，应用于线性系统的适定性和可控性

• 批准号: EP/I01621X/1
• 负责人: Jonathan Partington
• 金额: $ 2.96万
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI01621X%2F1
• 关键词: Spaces; analytic; functions; applied; well

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.

系统和控制理论是现代工程和应用数学的关键组成部分，包括与电网有关的问题，热方程以及动态系统的演变。该项目从纯数学（主要是复杂的分析和功能分析领域）开发工具，以分析三个基本概念：（i）可采用的方程式所需的方程式，以某种意义上说，管理系统的行为可以得到充分措施；（ ii）可控性，一种确切的方式，即可以通过适当的控制选择将系统转向任何所需行为的想法； （iii）可观察性，测量系统的属性产生了有关系统状态的完整信息。这些属性是在一般框架中研究的，这使人们能够分析许多类型的不断发展的行为。除了计划以上述应用程序动机开发的复杂分析和功能分析中的技术外，还计划追求使用最新结果数字理论中的最新结果以获取该领域的更多信息的想法。

项目成果

On Laplace-Carleson embedding theorems

关于拉普拉斯-卡尔森嵌入定理

• DOI: 10.48550/arxiv.1201.1021
• 发表时间: 2012
• 作者: Jacob B

Applications of Laplace-Carleson embeddings to admissibility and controllability

拉普拉斯-卡尔森嵌入在可容许性和可控性中的应用

• DOI: 10.48550/arxiv.1203.2666
• 发表时间: 2012
• 作者: Jacob B

Applications of Laplace--Carleson Embeddings to Admissibility and Controllability

拉普拉斯-卡尔森嵌入在可纳性和可控性中的应用

• DOI: 10.1137/120894750
• 发表时间: 2014
• 期刊: SIAM Journal on Control and Optimization
• 影响因子: 2.2
• 作者: Jacob B

Weighted multiple interpolation and the control of perturbed semigroup systems

加权多重插值与摄动半群系统的控制

• DOI: 10.1007/s00028-013-0184-4
• 发表时间: 2013
• 期刊: Journal of Evolution Equations
• 影响因子: 1.4
• 作者: Birgit Jacob;Jonathan R. Partington;Sandra Pott
• 通讯作者: Sandra Pott