HND下求解时变Sylvester方程的新神经网络  

A New Neural Network for Solving Time-Varying Sylvester Equation with Harmonic Noise Disturbance

作　　者：仓乃梦 郭东生 黎子豪 聂卓赟[2] CANG Nai-meng;GUO Dong-sheng;LI Zi-hao;NIE Zhuo-yun(School of Information and Communication Engineering,Hainan University,Haikou Hainan 570228,China;College of Information Science and Engineering,Huaqiao University,Xiamen Fujian 361021,China)

机构地区：[1]海南大学信息与通信工程学院,海南海口570228 [2]华侨大学信息科学与工程学院,福建厦门361021

出　　处：《计算机仿真》2025年第2期399-404,共6页Computer Simulation

基　　金：国家重点研发计划项目(2022ZD0119900);国家自然科学基金资助项目(U2141234);上海市“科技创新行动计划”项目(22015810300);海南省科技专项资助项目(ZDYF2021GXJS041)。

摘　　要：针对时变Sylvester方程在工程计算和信号处理等领域的实际应用中常常受到谐波噪声干扰而难以求解的问题,提出了一种基于内膜原理的神经网络(Internal Membrane Principle-based Neural Network,IMPNN),可以在谐波噪声干扰下求解时变Sylvester方程。首先,采用指数衰减公式来构建一个无噪声情况下的神经网络;然后基于内模原理设计了一个动态系统,该系统能够自动生成补偿谐波噪声干扰的信号;结合这个动态系统,进一步推导出IMPNN,它可以在存在谐波噪声情况下仍然有效地求解时变Sylvester方程;最后,通过设计单谐波噪声干扰和多谐波噪声干扰的对比仿真来验证所提出的IMPNN的有效性。仿真结果表明,提出的IMPNN可以更加准确、高效地求解时变Sylvester方程,从而为实际应用带来更大的便利和益处。A neural network based on the inner membrane principle(IMPNN)is proposed to solve the problem of difficulty in solving the time-varying Sylvester equation due to harmonic noise interference in practical applications such as engineering calculations and signal processing.The IMPNN can solve the time-varying Sylvester equation under harmonic noise interference.First,by using the exponential decay formula,the neural network is given to solve the time-varying Sylvester equation in the absence of noise.Then,based on the internal model theory,a dynamic system is designed that can generate compensation signals for harmonic noise interference.By combining such a dynamic system,the IMPNN is further derived for solving the time-varying Sylvester equation even in the presence of harmonic noise.Finally,single-harmonic and multi-harmonic noise interference simulation experiments are designed to verify the effectiveness of the proposed IMPNN.The simulation results show that the proposed neural network can solve time-varying Sylvester equations more accurately and efficiently,bringing greater convenience and benefits to practical applications.

关 键 词：谐波噪声 时变 神经网络 内模原理 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]