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态系统的分析（控制）设计和优化通常基于高维离散模型，因为它们结果例如从复杂几何形状上部分微分方程的有限元离散化。产生的普通微分方程的量通常很大（10000万），因此使数值计算效率不高。这激发了使用模型降低方法的使用。当模型通过子系统所产生的模型导致物理变量描述存储的能量时，在港口港口（pH）形式中对这种系统的建模尤其有利。因此，此模型类将是该项目的重点。一个目标是保留特征性的pH结构，以在随后的控制设计或耦合中利用。协会减少方法采用了该结构保存的自由度的相关部分，提供了更少的参数来提高近似质量。该项目的目的是在降低港口哈米尔顿港系统的结构模型订单中引入新的自由度，并将其扩展到该系统类别的一般状态空间模型的现有结果。此外，模型降低误差的严格和全局误差范围将扩展到降低 - 哈米尔顿港系统的降低。