Imitation learning presents an effective approach to alleviate the
resource-intensive and time-consuming nature of policy learning from scratch in
the solution space. Even though the resulting policy can mimic expert
demonstrations reliably, it often lacks predictability in unexplored regions of
the state-space, giving rise to significant safety concerns in the face of
perturbations. To address these challenges, we introduce the Stable Neural
Dynamical System (SNDS), an imitation learning regime which produces a policy
with formal stability guarantees. We deploy a neural policy architecture that
facilitates the representation of stability based on Lyapunov theorem, and
jointly train the policy and its corresponding Lyapunov candidate to ensure
global stability. We validate our approach by conducting extensive experiments
in simulation and successfully deploying the trained policies on a real-world
manipulator arm. The experimental results demonstrate that our method overcomes
the instability, accuracy, and computational intensity problems associated with
previous imitation learning methods, making our method a promising solution for
stable policy learning in complex planning scenarios.

通过引入稳定神经动力系统（SNDS），我们提出了一种保证稳定性的模仿学习方案，该方案通过联合训练策略和对应的 Lyapunov 候选者来构建具有正式稳定性保证的策略。我们在模拟环境中进行了广泛的实验并成功地将训练得到的策略部署于真实的机械臂，实验结果表明我们的方法解决了以往模仿学习方法中的不稳定性、准确性和计算强度问题，为复杂规划场景中的稳定策略学习提供了有希望的解决方案。