用自编码器构建可控制的低阶模型，提升系统预测与控制精度。
Learning Control-Affine Reduced-Order Models via Autoencoders
- 通过联合训练自编码器与状态空间模型，实现高维状态到低维隐空间的映射。
- 新模型在测试数据上预测误差更低，且能有效引导系统到达目标状态。
- 适合需高效建模与控制的复杂动态系统研究者使用。
本文提出一种识别控制仿射型降阶模型（ROM）的框架。该方法利用自编码器（AE）将高维状态和潜在的高维输入转换为适合控制仿射状态空间动力学的低维隐变量。通过同步训练自编码器与状态空间模型实现这一目标。此外，将离散ROM扩展为基于序列的模型，利用状态与输入的历史信息提升预测精度，同时保持控制仿射结构。通过反馈线性化原理验证模型有效性，并提供高效应用指南。在两个数值案例中评估所提框架性能，对比基准模型（即采用线性状态空间动力学的自编码器），评估内容包括测试数据上的预测精度及对系统进行轨迹或状态控制的有效性。
原文摘要 · Abstract (English)
We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state-space dynamics. This is achieved by simultaneous training of the AE and the state-space model. In addition, we extend the discrete ROM formulation to a sequence-based model, which processes state and input histories to improve prediction accuracy while preserving the control-affine structure. We motivate our framework by applying feedback linearization to the derived models, and we present guidelines for its efficient use. The proposed framework is assessed on two numerical examples and its performance is compared to a baseline model, where the AE identifies a latent space with linear state-space dynamics. The assessment involves evaluating the prediction accuracy of the ROM on test data and its effectiveness in controlling the system to a desired state or trajectory.
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