发表机构
Northwestern Polytechnical University（西北工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于Volterra级数和截断Laguerre展开的平衡截断方法，为双线性时滞系统定义近似Gramian，实现保结构模型降阶，并通过数值示例验证其效率。
AI 中文摘要
本文提出了一种平衡截断（BT）方法，用于实现双线性时滞系统的保结构模型降阶（MOR）。我们尝试基于Volterra级数理论为双线性时滞系统定义Gramian。在频域中明确给出了可控性和可观性Gramian，它们与双线性系统和时滞系统的Gramian一致。基于推导出的Gramian，我们提供了一种BT方法，以生成具有相同结构的降阶模型。我们还提出了一种基于截断Laguerre展开的数值求积规则，以对Gramian进行精确近似。所得近似Gramian的低秩结构极大地有利于整个MOR过程的高效执行。我们模拟了两个数值示例，以展示我们方法的效率。
英文摘要
A balanced truncation (BT) procedure is presented to achieve a structure-preserving model order reduction (MOR) for bilinear time-delay systems in this paper. We attempt to define Gramians for bilinear time-delay systems based on Volterra series theory. The controllability and observability Gramians in the frequency domain are given explicitly, which align with the ones of bilinear systems and time-delay systems. Based on the derived Gramians, a BT procedure is provided to produce reduced order models with the same structure. We also propose a numerical quadrature rule based on the truncated Laguerrre expansion to give an accurate approximation to Gramians. The resulting low-rank structure of approximate Gramians benefits a lot the efficient execution of the whole MOR procedure. Two numerical examples are simulated to showcase the efficiency of our approach.
