Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving precision in learning and ensuring the overall stability of the system. In response to this substantial challenge, this paper introduces a novel DS algorithm rooted in neural network technology. This algorithm not only possesses the capability to extract critical insights from demonstration data but also demonstrates the capacity to learn a candidate Lyapunov energy function that is consistent with the provided data. The model presented in this paper employs a straightforward neural network architecture that excels in fulfilling a dual objective: optimizing accuracy while simultaneously preserving global stability. To comprehensively evaluate the effectiveness of the proposed algorithm, rigorous assessments are conducted using the LASA dataset, further reinforced by empirical validation through a robotic experiment.

翻译：基于自主动态系统的算法在从演示学习（LfD）领域具有关键且基础性的作用。然而，这些算法面临着如何在实现学习精度与保证系统整体稳定性之间取得精妙平衡的重大挑战。针对这一重大挑战，本文提出了一种基于神经网络技术的新型动态系统算法。该算法不仅能够从演示数据中提取关键信息，还能学习与所提供数据一致的候选李雅普诺夫能量函数。本文提出的模型采用简单的神经网络架构，可出色地实现双重目标：在优化精度的同时保持全局稳定性。为全面评估所提算法的有效性，利用LASA数据集进行了严格评估，并通过机器人实验的实证验证进一步强化了评估结果。