时变二次规划的鲁棒归零神经网络求解模型

doi:10.12305/j.issn.1001-506X.2025.09.01

摘要/Abstract

摘要：

针对时变二次规划问题的离散时间归零神经网络求解模型中差分运算引入的噪声放大的问题，提出一种鲁棒的离散时间归零神经网络求解模型。首先，借助多项式预测滤波器，为差分运算建立状态空间模型。然后，利用对观测噪声鲁棒的卡尔曼滤波器，给出鲁棒微分器。当用该鲁棒微分器替代求解模型中的差分运算时，含噪观测对其影响在最大后验概率的意义下最小化。最后，通过仿真实验，验证了所提方法在性能上优于现有的离散时间归零神经网络求解模型，特别是在存在观测噪声条件下。

关键词: 时变二次规划, 归零神经网络, 多项式预测滤波器, 鲁棒微分器

Abstract:

To address the noise amplification problem caused by the differential operation in the discrete-time zeroing neural network solution model for time-varying quadratic programming, a robust discrete-time zeroing neural network solution model is proposed. Firstly, a state space model of the differential operation via a polynomial prediction filter is established. Secondly a robust differentiator is proposed by a Kalman filter robust to the observation noise. It is demonstrated that the impact of the noisy observations on the solution model can be minimized in the sense of maximum a posteriori probability when the proposed robust differentiator is employed to replace the differential operations in the solution model. Finally, the simulation experiments demonstrate that the proposed method gives superior performance compared to the existing discrete-time zeroing neural network solution models, especially in the presence of noisy observations.

Key words: time-varying quadratic programming （QP）, zeroing neural network, polynomial prediction filter, robust differentiator

中图分类号:

TP 183

黄庚, 李旦, 张建秋. 时变二次规划的鲁棒归零神经网络求解模型[J]. 系统工程与电子技术, 2025, 47(9): 2775-2784.

Geng HUANG, Dan LI, Jianqiu ZHANG. Robust zeroing neural network solution model for time-varying quadratic programming[J]. Systems Engineering and Electronics, 2025, 47(9): 2775-2784.

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模型	RMSE
DZNN求解式（12）	0.1176
DZNN求解式（13）	0.1273
RDZNN求解式（35）	0.0860
RDZNN求解式（36）	0.1381

模型	RMSE
DZNN求解式（12）	0.2516
DZNN求解式（13）	0.2948
RDZNN求解式（35）	0.1376
RDZNN求解式（36）	0.2127

模型	RMSE
模型	2Σ₁	4Σ₁	10Σ₁
RDZNN求解式（35）	0.1407	0.1403	0.1392
RDZNN求解式（36）	0.2045	0.2169	0.2132

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