Point-to-point and periodic motions are ubiquitous in the world of robotics. To master these motions, Autonomous Dynamic System (DS) based algorithms are fundamental in the domain of Learning from Demonstration (LfD). However, these algorithms face the significant challenge of balancing precision in learning with the maintenance of system stability. This paper addresses this challenge by presenting a novel ADS algorithm that leverages neural network technology. The proposed algorithm is designed to distill essential knowledge from demonstration data, ensuring stability during the learning of both point-to-point and periodic motions. For point-to-point motions, a neural Lyapunov function is proposed to align with the provided demonstrations. In the case of periodic motions, the neural Lyapunov function is used with the transversal contraction to ensure that all generated motions converge to a stable limit cycle. The model utilizes a streamlined neural network architecture, adept at achieving dual objectives: optimizing learning accuracy while maintaining global stability. To thoroughly assess the efficacy of the proposed algorithm, rigorous evaluations are conducted using the LASA dataset and a manually designed dataset. These assessments were complemented by empirical validation through robotic experiments, providing robust evidence of the algorithm's performance
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