Disturbance-Robust Dynamical System Learning With Neural ODEs and Flow-Matching Augmentation

Abstract

Autonomous dynamical systems (DS) are essential for imitation learning but often face challenges in simultaneously achieving high accuracy, stability guarantees, and resistance to disturbances. To overcome these limitations, this paper proposes a globally stable DS with trajectory attraction and disturbance robustness, termed K-Canyon DS (KCDS). The method first employs a Neural ODE to learn a diffeomorphic mapping from the task space to a linear latent space, thereby enhancing learning accuracy while ensuring global stability. Subsequently, based on clustering of starting points in the linear latent space, a nonlinear learnable trajectory-attractive field with a canyon-like structure is introduced to confer disturbance robustness. System parameters are trained via flow matching-based data augmentation, ultimately achieving a globally stable and disturbance-robust DS design. The proposed method is thoroughly evaluated on 2D and 3D LASA datasets, including comparative experiments with open-source baselines under disturbance. Real-robot experiments further demonstrate its practical applicability.