用动态模态分解方法实现大规模LPV系统高效建模。
Identifying Large-Scale Linear Parameter Varying Systems with Dynamic Mode Decomposition Methods
- 基于非侵入式降维的DMD-LPV方法，实现局部与全局识别。
- 在低维空间完成建模，性能几乎无损失，适用于大规模系统。
- 适合需要快速建模复杂非线性系统的工程师和研究人员。
线性参数变化（LPV）系统是一类成熟的非线性系统，具备丰富的稳定性分析、控制设计与响应求解理论。尽管已有数据驱动的LPV系统识别研究，但针对大规模系统的相关工作仍十分稀少。鉴于大规模系统在实践中普遍存在，本文提出一种基于非侵入式降维建模的局部与全局识别方法，称为DMD-LPV，其灵感源自动态模态分解（DMD）。为验证该方法，我们对一个由离散化线性扩散方程描述的系统进行了识别，其中扩散系数由参数的多项式定义。实验表明，所提方法可在无需全阶维度识别的前提下，高效构建大规模系统的降阶LPV模型，且在模型结构合理时性能几乎无衰减。
原文摘要 · Abstract (English)
Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven identification of such systems, the literature is quite scarce in terms of works that tackle the identification of LPV models for large-scale systems. Since large-scale systems are ubiquitous in practice, this work develops a methodology for the local and global identification of large-scale LPV systems based on nonintrusive reduced-order modeling. The developed method is coined as DMD-LPV for being inspired in the Dynamic Mode Decomposition (DMD). To validate the proposed identification method, we identify a system described by a discretized linear diffusion equation, with the diffusion gain defined by a polynomial over a parameter. The experiments show that the proposed method can easily identify a reduced-order LPV model of a given large-scale system without the need to perform identification in the full-order dimension, and with almost no performance decay over performing a reduction, given that the model structure is well-established.
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