用LSTM提升的深度库普曼模型，无须预设字典即可线性化带时延的非线性系统。
Deep Dictionary-Free Method for Identifying Linear Model of Nonlinear System with Input Delay
- 基于LSTM增强的深度库普曼模型，自动学习系统动态特征。
- 在未知真实非线性动力学下预测精度显著优于传统eDMD方法。
- 适合处理含时延的复杂非线性系统建模与控制问题。
带有输入延迟的非线性动力系统因其内在复杂性和延迟对系统行为的影响，在预测、估计和控制方面面临重大挑战。传统线性控制方法常在此类场景中失效，亟需创新方法。本文提出一种新方法，利用增强型长短期记忆（LSTM）的深度库普曼模型近似库普曼算子，实现带时间延迟的非线性系统的线性表示。通过引入LSTM层，该框架能捕捉历史依赖关系，并将时延系统动态高效编码至潜在空间。与依赖预设字典的传统扩展动态模式分解（eDMD）方法不同，该模型为无字典设计，避免了因先验动力学知识不准确导致的问题。在模拟系统上的定量对比表明，当真实非线性动力学未知时，其预测精度显著优于eDMD；而在已知系统动力学情况下，性能与eDMD相当。
原文摘要 · Abstract (English)
Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail in these contexts, necessitating innovative approaches. This paper introduces a novel approach to approximate the Koopman operator using an LSTM-enhanced Deep Koopman model, enabling linear representations of nonlinear systems with time delays. By incorporating Long Short-Term Memory (LSTM) layers, the proposed framework captures historical dependencies and efficiently encodes time-delayed system dynamics into a latent space. Unlike traditional extended Dynamic Mode Decomposition (eDMD) approaches that rely on predefined dictionaries, the LSTM-enhanced Deep Koopman model is dictionary-free, which mitigates the problems with the underlying dynamics being known and incorporated into the dictionary. Quantitative comparisons with extended eDMD on a simulated system demonstrate highly significant performance gains in prediction accuracy in cases where the true nonlinear dynamics are unknown and achieve comparable results to eDMD with known dynamics of a system.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。