基于深度学习的MIMO Wiener型Koopman模型识别
Identification of MIMO Wiener-type Koopman Models for Data-Driven Model Reduction using Deep Learning
摘要：
我们使用Koopman理论开发了一个数据驱动的多输入多输出（MIMO）输入仿射动力系统的非线性模型降阶和辨识策略。虽然目前的文献集中在线性和双线性Koopman模型，我们推导并使用维纳型Koopman制定。我们讨论了Wiener结构特别适合于模型降阶，并且可以自然地从Koopman理论导出。此外，维纳块结构统一了线性动力学块的数学简单性和双线性动力学的准确性。我们提出了一种结合自动编码器和线性动态的Koopman深度学习策略，该策略生成MIMO Wiener类型的低阶代理模型。在三个案例研究中，我们应用我们的框架识别和减少输入的多重性，化学反应器和高纯度蒸馏塔的系统。我们比较确定的维纳模型的预测性能的线性和双线性Koopman模型。我们观察到低阶维纳型Koopman模型的最高精度和最强的模型降阶能力，使其有希望的控制。
英文摘要：
We use Koopman theory to develop a data-driven nonlinear model reduction and identification strategy for multiple-input multiple-output (MIMO) input-affine dynamical systems. While the present literature has focused on linear and bilinear Koopman models, we derive and use a Wiener-type Koopman formulation. We discuss that the Wiener structure is particularly suitable for model reduction, and can be naturally derived from Koopman theory. Moreover, the Wiener block-structure unifies the mathematical simplicity of linear dynamical blocks and the accuracy of bilinear dynamics. We present a Koopman deep-learning strategy combining autoencoders and linear dynamics that generates low-order surrogate models of MIMO Wiener type. In three case studies, we apply our framework for identification and reduction of a system with input multiplicity, a chemical reactor and a high-purity distillation column. We compare the prediction performance of the identified Wiener models to linear and bilinear Koopman models. We observe the highest accuracy and strongest model reduction capabilities of low-order Wiener-type Koopman models, making them promising for control.
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