【摘要】 设计了两类求解常微分方程的零化神经网络．把常微分方程重写为向量值不确定误差函数，将向量值不确定误差函数代入零化神经网络设计公式中，提出了一类求解常微分方程的连续时间零化神经网络，其指数收敛于零．针对潜在的数字硬件实现，通过对连续时间零化神经网络进行离散化，设计了一类离散时间零化神经网络，给出了充要条件来保证离散时间神经网络生成的序列以截断误差为O (τ~2)（τ>0表示采样周期）收敛到零．通过两个数值实验验证了连续时间零化神经网络和离散时间零化神经网络的有效性．更多还原

【Abstract】 Two types of zeroing neural networks are proposed for solving ordinary differential equations.By rewriting ordinary differential equations into vector valued uncertain error functions,substituting vector valued uncertain error functions into the zeroing neural network design formula,a class of continuous time zeroing neural networks for solving ordinary differential equations is proposed,which converges to zero exponentially. For potential digital hardware realization,a class of discrete-time neural networks was designed by discretizing the continuous time zeroing neural network.At the same time,sufficient and necessary conditions are provided to ensure that the sequence generated by the discrete-time neural network converges to zero with a truncation error ofO(τ2)（τ >0 denoting the sampling period）.The effectiveness of continuous time zeroing neural networks and discrete-time zeroing neural networks was verified through two numerical experiments.更多还原