提出递归算法实现神经状态空间模型在线学习，高效且准确。
Online learning of neural state-space models
- 基于子空间编码器设计递归识别算法，支持在线更新。
- 仿真验证表明算法在保持高精度的同时计算效率高。
- 适合需要实时系统建模与自适应的场景，如控制与预测。
基于深度学习的非线性系统辨识近年来取得进展，采用编码器估计神经状态空间（ANN-SS）模型，在离线设置下通过历史输入输出数据估计初始模型状态，达到当前最佳性能。这些方法通常用于多射击式离线辨识，而此类模型的在线学习仍鲜有研究。本文提出一种分批学习流程和针对子空间编码器的直接递归辨识算法。我们对递归形式进行了收敛性分析，并通过大量仿真验证其性能。结果表明，所提方法可实现计算高效的在线自适应，同时保持高模型精度。
原文摘要 · Abstract (English)
Recent advances in deep-learning-based nonlinear system identification have led to encoder-based estimation of neural state-space (ANN-SS) models that achieve state-of-the-art performance in offline settings by estimating initial model states from past input-output data. These methods are typically used in multiple-shooting-based offline identification, and online learning of these models remains largely unexplored. This paper presents a batch-wise learning pipeline and a direct recursive identification algorithm for subspace encoder-based ANN-SS models. We provide convergence analysis of the recursive formulation and validate its performance through extensive simulation studies. The results demonstrate that the proposed approach enables computationally efficient online adaptation with high model accuracy.
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