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To calculate the time-varying Lyapunov equation (TVLE), a novel varying-parameter neural dynamics (termed as NVPND) is presented and analyzed. We specifically address the following three important issues: 1. Stability of NVPND to ensure the validity of the solution; 2. The robustness against various disturbances to guarantee the capability of NVPND in additive environment; 3. Super-exponential convergent performance to endow NVPND for faster convergent rate. Unlike the traditional Zhang neural dynamics (termed as ZND), the newly proposed neural formula employs a super-exponential convergent speed and the strong tolerance for undesired noises. Various comparisons for solving time-varying Lyapunov equation are carried out and substantiates the effectiveness of the proposed NVPND model. Finally, physical examples for repetitive trajectory planning of a redundant manipulator further substantiate the theoretical proofs and physical applications.

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Solution for Lyapunov Equation by a Novel Varying-Parameter Neural Dynamics with Its Kinematic Application to Redundant Manipulators

  • 会议论文

  • 发表日期：

    2026年

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  • Yi Yu,
  • Junjie Hao,
  • Ying Kong

摘要

To calculate the time-varying Lyapunov equation (TVLE), a novel varying-parameter neural dynamics (termed as NVPND) is presented and analyzed. We specifically address the following three important issues: 1. Stability of NVPND to ensure the validity of the solution; 2. The robustness against various disturbances to guarantee the capability of NVPND in additive environment; 3. Super-exponential convergent performance to endow NVPND for faster convergent rate. Unlike the traditional Zhang neural dynamics (termed as ZND), the newly proposed neural formula employs a super-exponential convergent speed and the strong tolerance for undesired noises. Various comparisons for solving time-varying Lyapunov equation are carried out and substantiates the effectiveness of the proposed NVPND model. Finally, physical examples for repetitive trajectory planning of a redundant manipulator further substantiate the theoretical proofs and physical applications.