  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.
