基于非线性激活函数的零化神经网络及其在动态问题求解中的应用  

Nonlinear Activation Function and Its Application on Solving Dynamic Problems Based on Zeroing Neural Network

作　　者：刘万太[1] 练红海 王芳[1] 李谟发[1] 邓鹏[1] LIU Wantai;LIAN Honghai;WANG Fang;LI Mofa;DENG Peng(School of Wind Energy Engineering,Hunan Electrical College of Technology,Xiangtan 411101;School of Information and Electrical Engineering,Hunan University of Science and Technology,Xiangtan 411201)

机构地区：[1]湖南电气职业技术学院风能工程学院,湘潭411101 [2]湖南科技大学信息与电气工程学院,湘潭411201

出　　处：《系统科学与数学》2024年第7期1870-1884,共15页Journal of Systems Science and Mathematical Sciences

基　　金：湖南省自然科学基金(2021JJ50018,2022JJ60023,2023JJ60177);湖南省教育厅科学研究项目(22B0955)资助课题。

摘　　要：零化神经网络(zeroing neural network,ZNN)因其具有快速的收敛速度和较为出色的抗外界噪声干扰的能力,自被提出以来就有大量研究且广泛地应用于时变问题的求解.然而,目前所存在的零化神经网络模型的收敛速度和抗干扰能力仍然不尽如人意.因此,为进一步提高零化神经网络的性能,文章提出了一种固定时间收敛激活函数(fixed-time convergent activation function,FTCAF),然后,基于该激活函数建立了固定时间收敛的零化神经网络(fixed-time convergent zeroing neural network,FTCZNN)模型,并应用该模型对动态Sylvester方程(dynamic Sylvester equation,DSE)进行求解.理论分析证明了FTCZNN模型拥有固定的时间收敛上界和较为出色的抗外界噪声干扰的能力.此外,DSE数值仿真实验也证明了FTCZNN模型的优越性能.最后,FTCZNN模型被用于机械臂的轨迹跟踪实验,且实验结果再次证明了FTCZNN模型相较于传统ZNN模型拥有快速的收敛速度和较为出色的抗干扰能力,因此其实际应用能力也得到了验证.Zeroing neural network(ZNN)has been widely used to solve time-varying problems since it was proposed because of its fast convergence speed and ability to resist external noise interference.However,the convergence speed and anti-interference ability of the existing zeroing neural network models are still not satisfactory.Therefore,to further improve the performance of ZNN,a new fixed-time convergent activation function(FTCAF)is designed in this paper.Then,a fixed-time convergent zeroing neural network(FTCZNN)model is established based on the proposed activation function and this model is applied to solve dynamic Sylvester equation(DSE).Theoretical analysis proves that the FTCZNN model has a fixed time convergence upper limit and strong anti-interference ability.In addition,numerical simulation results also demonstrate the superior performance of the FTCZNN model.Finally,FTCZNN model is used to realize the trajectory tracking experiment of the robot manipulator.The experimental results once again prove that the FTCZNN model has fast convergence speed and strong anti-interference ability,and its practical application ability is also verified.

关 键 词：零化神经网络 激活函数 动态Sylvester方程 机械臂轨迹跟踪 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]