改进的梯度神经网络求解源于Lyapunov矩阵方程的一类方程  

Improved Gradient Neural Networks for Online Solution Derived from Lyapunov Matrix Equation a Class of Equations

作　　者：王璐 夏吾才让[1] WANG Lu;Xiawucairang(School of Mathematics and Computer Science,Northwest Minzu University,Lanzhou 730030,China)

机构地区：[1]西北民族大学数学与计算机科学学院,甘肃兰州730030

出　　处：《西北民族大学学报（自然科学版）》2020年第3期79-83,共5页Journal of Northwest Minzu University(Natural Science)

摘　　要：运用一种不同类型行为函数的梯度神经网络来求解源于Lyapunov矩阵方程的一类方程.通过理论分析,发现任何单调递增的奇行为函数可用于梯度神经网络的构造且改进后的梯度神经网络模型具有全局收敛性.此外,当使用power-sigmoid行为函数时,梯度神经网络模型与线性神经网络模型相比具有超收敛性.By adding different activation functions a type of gradient neural networks is developed and presented for the online solution derived from Lyapunov matrix equation for a class of equations.Theoretical analysis showed that any monotonically increasing odd activation function could be used in the construction of neural networks and the improved neural models have the global convergence performance.Moreover,neural networks have superior convergence when compared to linear models when the power-sigmoid activation functions were used.

关 键 词：梯度神经网络 行为函数 LYAPUNOV矩阵方程 全局收敛 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] V249.121[自动化与计算机技术—控制科学与工程]