发表机构
Indian Institute of Science（印度科学理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非线性机械系统，提出结构保持的端口-哈密顿库普曼框架，通过动量变换和神经架构学习无源动力学，实现高精度预测与控制。
AI 中文摘要
有限维库普曼模型能够实现对非线性机器人系统的高效线性预测和控制。然而，仅从轨迹数据学习的模型可能违反底层力学的能量结构，产生表现出人为能量增长并在递归传播下发散的预测。本工作提出了一种基于广义动量坐标的欧拉-拉格朗日系统的结构保持库普曼框架。动量变换将机械驱动揭示为已知的、与状态无关的端口，该端口在提升动力学中被显式保留。开发了一种结构约束的神经架构，用于联合学习提升函数和端口-哈密顿库普曼生成器，使得学习到的动力学通过构造而非通过惩罚项或事后投影而具有无源性。Cayley-中点离散化进一步在离散时间中精确保持相应的存储-耗散平衡。通过推导离散存储平衡和所学预测器的相关稳定性保证，分析性地确立了这些性质。仿真和实验研究表明，与库普曼基线相比，预测精度、数据效率和闭环跟踪性能均有提高，且对于更高维系统，增益越来越大。
英文摘要
Finite-dimensional Koopman models enable efficient linear prediction and control of nonlinear robotic systems. However, models learned purely from trajectory data may violate the energetic structure of the underlying mechanics, producing predictions that exhibit artificial energy growth and diverge under recursive propagation. This work presents a structure-preserving Koopman framework for Euler-Lagrange systems built on generalized-momentum coordinates. The momentum transformation exposes the mechanical actuation as a known, state-independent port, which is preserved explicitly in the lifted dynamics. A structure-constrained neural architecture is developed to jointly learn the lifting functions and a port-Hamiltonian Koopman generator, rendering the learned dynamics passive by construction rather than through penalty terms or post-hoc projection. A Cayley-midpoint discretization further preserves the corresponding storage-dissipation balance exactly in discrete time. These properties are established analytically by deriving the discrete storage balance and associated stability guarantees of the learned predictor. Simulation and experimental studies demonstrate improved prediction accuracy, data efficiency, and closed-loop tracking over Koopman baselines, with increasing gains for higher-dimensional systems.
