ABSTRACT

We present a new structure-preserving model order reduction (MOR) framework for large-scale port-Hamiltonian descriptor systems (pH-DAEs). Our method exploits the structural properties of the Rosenbrock system matrix for this system class and utilizes condensed forms which often arise in applications and reveal the solution behaviour of a system. Provided that the original system has such a form, our method produces reduced-order models (ROMs) of minimal dimension, which tangentially interpolate the original model’s transfer function and are guaranteed to be again in pH-DAE form. This allows the ROM to be safely coupled with other dynamical systems when modelling large system networks, which is useful, for instance, in electric circuit simulation.

摘要

我们为大规模端口哈密尔顿描述符系统（pH-DAE）提出了一种新的结构保留模型降阶（MOR）框架。我们的方法利用该系统类的 Rosenbrock 系统矩阵的结构特性，并利用应用程序中经常出现的压缩形式并揭示系统的解决方案行为。假设原始系统具有这样的形式，我们的方法会生成最小维度的降阶模型（ROM），该模型对原始模型的传递函数进行切向插值，并保证再次采用 pH-DAE 形式。这使得 ROM 在对大型系统网络进行建模时能够安全地与其他动态系统耦合，这在电路仿真等领域很有用。