标题： 数据驱动的平衡截断各种推广的实现 显示英文标题

标题： Data-driven Implementations of Various Generalizations of Balanced Truncation

摘要： 存在两种主要的非侵入式近似平衡截断实现框架：基于求积的框架和基于ADI的框架。 这两种方法仅依赖于传递函数的样本来构建截断的平衡模型，从而不需要访问原始模型的状态空间实现。 最近，基于求积的框架已被扩展到平衡截断的各种推广形式，包括正实平衡截断、有界实平衡截断和平衡随机截断。 虽然这种扩展在理论上是非侵入式的——意味着它不需要原始状态空间实现——但它依赖于传递函数的谱因子化的样本。 由于目前尚无获取此类样本的实际方法，因此这种扩展仍然主要是理论上的贡献。 在本工作中，我们提出了一种非侵入式的ADI型框架，用于这些广义平衡截断方法，该框架在实现时只需原始传递函数的样本。 显示英文摘要

摘要： There exist two main frameworks for non-intrusive implementations of approximate balanced truncation: the quadrature-based framework and the ADI-based framework. Both approaches rely solely on samples of the transfer function to construct truncated balanced models, eliminating the need for access to the original model's state-space realization. Recently, the quadrature-based framework has been extended to various generalizations of balanced truncation, including positive-real balanced truncation, bounded-real balanced truncation, and balanced stochastic truncation. While this extension is theoretically nonintrusive-meaning it does not require the original state-space realization-it depends on samples of spectral factorizations of the transfer function. Since practical methods for obtaining such samples are currently unavailable, this extension remains largely a theoretical contribution. In this work, we present a non-intrusive ADI-type framework for these generalized balanced truncation methods that requires only samples of the original transfer function for implementation.