用神经网络建模哈密顿系统，同时保持结构与多平衡点稳定性。
Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems
- 放松凸性约束，提升模型表达能力
- 可学习多个稳定平衡点，优于传统单平衡点方法
- 适合需要物理一致性建模的控制系统研究
本文研究数据驱动建模端口-哈密顿系统时保持其内在哈密顿结构和稳定性属性的问题。提出一种新型基于神经网络的端口-哈密顿建模方法，放宽了神经网络哈密顿近似中常见的凸性约束，从而提升了模型的表达能力和泛化性能。通过去除该限制，新方法允许使用更通用的非凸哈密顿表示，增强建模灵活性与准确性。此外，该方法在学习过程中融入稳定平衡点信息，使所学模型能够保持多个孤立平衡点的稳定性，而非局限于传统方法中的单一平衡点。通过两个数值实验验证了所提方法的有效性，结果表明其在结构与稳定性保持方面优于基线方法。
原文摘要 · Abstract (English)
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling technique that relaxes the convexity constraint commonly imposed by neural network-based Hamiltonian approximations, thereby improving the expressiveness and generalization capability of the model. By removing this restriction, the proposed approach enables the use of more general non-convex Hamiltonian representations to enhance modeling flexibility and accuracy. Furthermore, the proposed method incorporates information about stable equilibria into the learning process, allowing the learned model to preserve the stability of multiple isolated equilibria rather than being restricted to a single equilibrium as in conventional methods. Two numerical experiments are conducted to validate the effectiveness of the proposed approach and demonstrate its ability to achieve more accurate structure- and stability-preserving learning of port-Hamiltonian systems compared with a baseline method.
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