求解时变二次规划的抗噪终态零化神经网络：一种三幂次加速策略

仲国民; 肖里坤; 汪黎明; 孙明轩

doi:10.11999/JEIT250128

求解时变二次规划的抗噪终态零化神经网络：一种三幂次加速策略

doi: 10.11999/JEIT250128 cstr: 32379.14.JEIT250128

仲国民^{1, 2, ,},
肖里坤¹,
汪黎明¹,
孙明轩¹

1.
浙江工业大学信息工程学院杭州 310023
2.
浙江工业大学先进技术研究院杭州 310014

基金项目: 国家自然科学基金 (62073291, 62222315)

详细信息

作者简介:
仲国民：男，讲师，研究方向为系统辨识、迭代学习控制和神经计算

肖里坤：男，硕士生，研究方向为神经计算和机械臂运动规划

汪黎明：男，博士生，研究方向为神经计算和机械臂运动规划

孙明轩：男，教授，研究方向为学习系统和神经计算

通讯作者:
仲国民　zgm@zjut.edu.cn

中图分类号: TN911;TP183
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- 被引次数: 0
出版历程
- 收稿日期: 2025-03-05
- 修回日期: 2025-08-28
- 网络出版日期: 2025-09-02

Noise-Tolerant Terminal Zeroing Neural Networks for Solving Time-Varying Quadratic Programming: A Triple Power-Rate Speeding-Up Strategy

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
2.
Academy for Advanced Interdisciplinary Science and Technology, Zhejiang University of Technology, Hangzhou 310014, China

Funds: The National Natural Science Foundation of China (62073291, 62222315)

摘要

摘要: 针对时变等式约束的二次规划问题，该文提出三幂次加速的抗噪终态零化神经网络，实现神经计算误差固定时间收敛。相比于常规双幂次型终态零化神经网络，所提网络收敛速度更快，抗噪性能更强。分析不同参数情况下的收敛过程并给出具体的收敛时间表达式；理论证明该神经网络系统对渐消噪声具有抑制能力。针对冗余机械臂重复运动规划问题，采用三幂次加速的抗噪终态零化神经网络作为求解器，实现固定时间获取末端执行器的期望轨迹。考虑重复运动规划中定常增益优化指标的局限性，设计时变增益优化指标以提高冗余机械臂作业效率。时变二次规划和冗余机械臂的数值仿真结果分别验证三幂次加速的抗噪终态零化神经网络和时变增益优化指标的有效性。
- 零化神经网络 /
- 三幂次激活函数 /
- 二次规划 /
- 重复运动规划
Abstract: Objective The computational performance of Zeroing Neural Networks (ZNNs) is enhanced by introducing additional power terms into the activation function. However, this strategy complicates the derivation of explicit settling time expressions. To address this issue, a triple power-rate activation function is designed, and a power-rate speeding-up noise-tolerant terminal ZNN is constructed, through which an exact expression for the settling time is derived. In previous studies, the optimization criterion parameter for repetitive motion planning was typically constant, which may reduce the operational efficiency of robotic manipulators. To overcome this limitation, a time-varying parameter optimization criterion is developed to satisfy task requirements at different stages of repetitive motion planning, thereby improving the operational efficiency of redundant robotic manipulators during task execution. Methods A triple power-rate activation function is proposed, extending the conventional bi-power activation function, and a power-rate speeding-up noise-tolerant terminal ZNN is constructed. The convergence process under different parameter settings is analyzed, and explicit settling time expressions are derived. Theoretical analysis confirms that the proposed neural network can effectively suppress vanishing noise. For the repetitive motion planning problem of redundant manipulators, the power-rate speeding-up noise-tolerant terminal ZNN is employed as a solver to ensure acquisition of the desired end-effector trajectory within fixed time. To address the limitations of constant-parameter optimization criteria in repetitive motion planning, a time-varying parameter optimization criterion is designed, which demonstrably improves the operational efficiency of redundant manipulators. Results and Discussions In this study, the power-rate speeding-up noise-tolerant terminal ZNN is employed together with bi-power-rate terminal ZNNs to solve time-varying quadratic programming problems. Simulation results show that the proposed power-rate speeding-up noise-tolerant terminal ZNN achieves a faster convergence rate (Fig.2(a), Fig.2(b)) and demonstrates improved capability in suppressing vanishing noise (Fig.2(c)). The convergence process of neural computational error under different parameter conditions is analyzed without noise (Fig 3). Furthermore, the power-rate speeding-up noise-tolerant terminal ZNN is applied to the repetitive motion planning problem of redundant manipulators. Its effectiveness in solving repetitive motion planning is validated (Fig. 4), and the integration of a time-varying parameter optimization criterion further enhances the operational efficiency of redundant manipulators (Fig. 5). Conclusions A power-rate speeding-up noise-tolerant terminal ZNN is proposed for solving time-varying quadratic programming problem with time-varying equality constraints, ensuring fixed time convergence of neural computing errors. Compared with conventional bi-power-rate terminal ZNNs, the proposed network achieves faster convergence and stronger noise-tolerance performance. To address the limitations of constant-parameter optimization criteria in repetitive motion planning, a time-varying parameter optimization criterion is designed and shown to improve the operational efficiency of redundant manipulators.
- Zeroing Neural Networks (ZNNs) /
- Triple power-rate activation function /
- Quadratic programming /
- Repetitive motion planning.

HTML全文

图 1 TPTZNN电路参考图

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图 2 6种ZNN求解时变二次规划

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图 3 不同参数情况下TPTZNN的误差收敛过程

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图 4 TPTZNN求解冗余机械臂重复运动规划

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图 5 时变增益指标下冗余机械臂重复运动规划

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