  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.
