ABSTRACT Motivated by the challenges of designing feedback controllers for spatially distributed systems, we present an efficient approach to obtaining the frequency response of such systems, from which low-order models can be identified. This is achieved by combining the frequency responses of constituent lower-order subsystems in a way that exploits the interconnectivity arising from spatial discretisation. This approach extends to the singular subsystems that arise upon spatial discretisation of systems governed by PDAEs, with fluid flows being a prime example. The main result of this paper is a proof that the computational complexity of forming the overall frequency response is minimised if the subsystems are merged in a particular fashion. Doing so reduces the complexity by several orders of magnitude; a result demonstrated upon the numerical example of a spatially discretised wave-diffusion equation. By avoiding the construction, storage, or manipulation of large-scale system matrices, this modelling approach is well conditioned and computationally tractable for spatially distributed systems consisting of enormous numbers of subsystems, therefore bypassing many of the problems with conventional model reduction techniques.

中文翻译：

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用于空间分布式系统低阶建模的高效频率响应计算

摘要受为空间分布式系统设计反馈控制器的挑战所激发，我们提出了一种获得此类系统频率响应的有效方法，从中可以识别低阶模型。这是通过以利用空间离散化产生的互连性的方式组合组成低阶子系统的频率响应来实现的。这种方法扩展到由 PDAE 控制的系统的空间离散化产生的奇异子系统，流体流动是一个主要例子。本文的主要结果证明，如果子系统以特定方式合并，则形成整体频率响应的计算复杂性将最小化。这样做可以将复杂性降低几个数量级；在空间离散波扩散方程的数值示例上证明的结果。通过避免大规模系统矩阵的构建、存储或操作，这种建模方法适用于由大量子系统组成的空间分布式系统，并且在计算上易于处理，因此绕过了传统模型简化技术的许多问题。