Learning a stable dynamic system (DS) encoding human motion rules has been shown as an efficient approach for transferring motion skills. However, contradictions always exist between the stability, accuracy and generalization of the learned DS. This paper presents an approach to enhance the accuracy and generalization by learning a neural-shaped quadratic Lyapunov function (NS-QLF). For the stability concern, the NS-QLF is designed to satisfy LF basic properties. Thanks to the flexibility of the neural network, the NS-QLF shape can capture motion rules in a broad area. The corresponding neural-learning problem is formulated as a convex optimization problem. We then learn an original DS (ODS) by using the Gaussian process regression (GPR) algorithm and stabilize the ODS by solving an NS-QLF-constrained convex optimization problem. The resulted stable DS (SDS) can not only accurately reproduce trajectories near the demonstration area, but also can utilize the NS-QLF shape information to enhance the generalization capacity in regions away from the demonstration area. Various comparative simulations and experiments are conducted to show the benefits of the presented approach.

学习编码人体运动规则的稳定动态系统 (DS) 已被证明是转移运动技能的有效方法。然而，学习到的 DS 的稳定性、准确性和泛化性之间始终存在矛盾。本文提出了一种通过学习神经型二次李雅普诺夫函数 (NS-QLF) 来提高准确性和泛化能力的方法。出于稳定性考虑，NS-QLF 被设计为满足 LF 的基本属性。得益于神经网络的灵活性，NS-QLF 形状可以捕捉广阔区域的运动规则。相应的神经学习问题被表述为凸优化问题。然后，我们使用高斯过程回归 (GPR) 算法学习原始 DS (ODS)，并通过求解 NS-QLF 约束凸优化问题来稳定 ODS。由此产生的稳定 DS (SDS) 不仅可以准确地再现示范区附近的轨迹，还可以利用 NS-QLF 形状信息来增强远离示范区的区域的泛化能力。进行了各种比较模拟和实验以显示所提出方法的好处。