Analysis and computation of stability exponents for port-Hamiltonian delay differential-algebraic equations (A02)

端口哈密尔顿时滞微分代数方程稳定性指数的分析与计算（A02）

• 批准号: 193240938
• 金额: --
• 依托单位: Fachgebiet Numerische Mathematik
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/193240938?language=en
• 关键词: Analysis; computation; stability; exponents; port

Delay differential-algebraic equations (DDAEs) arise in a variety of applications including flow control, biological systems, and power networks. In many of the applications it is advantageous to formulate the DDAEs via a model hierarchy of port-Hamiltonian (pH) DDAE models. We will study existence, uniqueness and sensitivity for such pHDDAEs, in particular those where the interconnection of subsystems is delayed. We will derive vari-ational formulations and study the resulting operator pH DDAEs with respect to space-time discretization and control. In particular we will derive model reduction techniques and methods for the estimation of stability regions for pHDDAEs.

延迟微分代数方程（DDAE）出现在各种应用中，包括流量控制，生物系统和电力网络。在许多应用中，通过端口-哈密尔顿（pH）DDAE模型的模型层次来公式化DDAE是有利的。我们将研究这种pHDDAE的存在性，唯一性和灵敏度，特别是那些子系统的互连延迟。我们将推导出变分公式，并研究由此产生的运营商pH DDAE相对于时空离散化和控制。特别是，我们将推导出模型简化技术和方法，用于估计pHDDAE的稳定区域。