New degrees of freedom and rigorous error bounds for the structure-preserving model order reduction of port-Hamiltonian systems

端口哈密尔顿系统的结构保持模型降阶的新自由度和严格误差界限

• 批准号: 418612884
• 负责人: Professor Dr.-Ing. Boris Lohmann
• 金额: --
• 依托单位: Lehrstuhl für Regelungstechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/418612884?language=en
• 关键词: New; degrees; freedom; rigorous; error

The analysis, (control) design and optimization of dynamical systems with spatially distributed parameters is often based on high-dimensional discretized models, as they result e.g. from a finite element discretization of partial differential equations over a complex geometry. The amount of resulting ordinary differential equations is often very large (10.000 up to 1 million), hence making numerical computations unefficient. This motivates the use of model order reduction methods. Modelling of such systems in port-Hamiltonian (pH) form is particularly advantageous when the models result by thecoupling of subsystems, in which the physical variables describe the energy stored. Therefore, this model class will be the focus of this project. One goal is to preserve the characteristic pH-structure, to be taken advantage of in a subsequent control design or coupling. Convential reduction methods employ a relevant part of the availabledegrees of freedom for this structure preservation, providing less parameters to increase the approximation quality. The goal of this project is to introduce new degrees of freedom in the structure-preserving model order reduction of port-Hamiltonian systems andhence to extend existing results for general state-space models to this system class. Further, rigorous and global error bounds for the model reduction error are to be extended to the reduction of port-Hamiltonian systems.

具有空间分布参数的动力系统的分析、（控制）设计和优化通常基于高维离散模型，因为它们的结果例如：来自复杂几何上的偏微分方程的有限元离散。所得常微分方程的数量通常非常大（10,000 到 100 万），因此使得数值计算效率低下。这激发了模型降阶方法的使用。当模型由子系统耦合产生时，以端口哈密尔顿 (pH) 形式对此类系统进行建模特别有利，其中物理变量描述存储的能量。因此，该模型类将是本项目的重点。目标之一是保留特有的 pH 结构，以便在后续控制设计或耦合中加以利用。传统的简化方法采用可用自由度的相关部分来保存这种结构，提供较少的参数来提高近似质量。该项目的目标是在端口哈密尔顿系统的结构保持模型降阶中引入新的自由度，从而将一般状态空间模型的现有结果扩展到此类系统。此外，模型缩减误差的严格和全局误差界限将扩展到端口哈密尔顿系统的缩减。