Low-Order Parametric State-Space Modeling of MIMO Systems in the Loewner Framework

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-11-17 DOI:10.1137/22m1509898

Tea Vojkovic, David Quero, Charles Poussot-Vassal, Pierre Vuillemin

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引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3130-3164, December 2023.
Abstract.In this work, we present a novel data-driven method for identifying parametric MIMO generalized state-space or descriptor systems of low order that accurately capture the frequency and time domain behavior of large-scale linear dynamical systems. The low-order parametric descriptor systems are identified from transfer matrix samples by means of two-variable Lagrange rational matrix interpolation. This is done within the Loewner framework by deploying the new matrix-valued barycentric formula given in both right and left polynomial matrix fraction forms, which enables the construction of minimal parametric descriptor systems with rectangular transfer matrices. The developed method allows the reduction of order and parameter dependence complexity of the constructed system. Stability of the system is preserved by the postprocessing technique based on flipping signs of unstable poles. The developed methodology is illustrated with a few academic examples and applied to low-order parametric state-space identification of an aerodynamic system.

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Loewner框架下MIMO系统的低阶参数状态空间建模

应用动力系统学报，第22卷，第4期，3130-3164页，2023年12月。摘要。在这项工作中，我们提出了一种新的数据驱动方法，用于识别参数MIMO广义状态空间或低阶描述系统，该系统可以准确捕获大规模线性动力系统的频率和时域行为。采用双变量拉格朗日有理矩阵插值方法，从传递矩阵样本中识别出低阶参数广义系统。这是在Loewner框架内完成的，通过部署以右和左多项式矩阵分数形式给出的新的矩阵值质心公式，这使得具有矩形转移矩阵的最小参数描述子系统的构建成为可能。该方法降低了构造系统的阶数和参数依赖复杂性。采用基于不稳定极点翻转符号的后处理技术，保持了系统的稳定性。最后通过几个实例说明了所开发的方法，并将其应用于气动系统的低阶参数状态空间辨识。

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来源期刊

SIAM Journal on Applied Dynamical Systems 物理-物理：数学物理

CiteScore

3.60

自引率

4.80%

发文量

审稿时长

6 months

期刊介绍： SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and its application to the physical, engineering, life, and social sciences. SIADS is published in electronic format only.