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When encoding robotic tasks through autonomous dynamical systems (DSs) represented as velocity fields, neural networks serve as ideal modeling tools due to their powerful nonlinear approximation capabilities. However, existing neural network-based methods guarantee only local asymptotic stability. To overcome this limitation, we propose a global asymptotic stability DSs constructed around a symmetric negative definite matrix generation network (SNDM-GenNet). This neural architecture leverages inverse Cholesky Decomposition to enforce symmetric negative definiteness on its output matrix. Through Lyapunov stability theory, we rigorously prove the global convergence of all system trajectories to the target equilibrium. Validation on the LASA handwriting dataset and experiments on a 6-DOF collaborative robot (Chinrobo CRB-7) confirm the method’s efficacy.

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Learning Stable Nonlinear Dynamical Systems with Symmetric Negative Definite Matrix Generation Network

  • 会议论文

  • 发表日期：

    2026年

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  • Tianxiang Jiang,
  • Pingyun Nie,
  • Jiexin Zhang,
  • Erxuan Xie,
  • Huaiwu Zou,
  • Bo Zhang

摘要

When encoding robotic tasks through autonomous dynamical systems (DSs) represented as velocity fields, neural networks serve as ideal modeling tools due to their powerful nonlinear approximation capabilities. However, existing neural network-based methods guarantee only local asymptotic stability. To overcome this limitation, we propose a global asymptotic stability DSs constructed around a symmetric negative definite matrix generation network (SNDM-GenNet). This neural architecture leverages inverse Cholesky Decomposition to enforce symmetric negative definiteness on its output matrix. Through Lyapunov stability theory, we rigorously prove the global convergence of all system trajectories to the target equilibrium. Validation on the LASA handwriting dataset and experiments on a 6-DOF collaborative robot (Chinrobo CRB-7) confirm the method’s efficacy.