论文标题
零神经网络：通过ZNN进行时变矩阵问题的预测计算简介
Zeroing Neural Networks : an Introduction to Predictive Computations for Time-varying Matrix Problems via ZNN
论文作者
论文摘要
本文希望增加我们对时间的理解和计算知识 - 各种矩阵问题和张神经网络（ZNNS）。这些神经网络是针对时间或单个参数发明的 - 2001年左右在中国临近矩阵问题，几乎所有的进步已经取得了进步，并且最多仍然来自其出生地。 Zhang神经网络方法已成为解决离散传感器驱动时间的骨干 - 在中国的控制理论和其他工程应用中，在实时，理论上和ON上的矩阵问题各不相同。它们已成为许多时间的选择方法 - 各种矩阵问题，这些问题受益于或需要有效，准确和预测的实时计算。典型的张神经网络算法在其初始设置中需要七个不同的步骤。离散化Zhang神经网络算法的构建从具有相关误差方程的模型方程式开始，并规定了误差函数快速降低。然后，将误差函数微分方程与收敛的外观有限差差公式配对，以创建一个明显的新的多步骤样式求解器，该公式可以可靠地从当前和早期的状态和解决方案数据中可靠地预测系统的未来状态。随时间变化的矩阵问题的离散化Zhang神经网络算法的MATLAB代码通常由一个线性方程组成，每个时间步骤求解一个已有数据的递归。这使得基于Zhang神经网络的离散算法具有高度竞争性的，具有普通微分方程的初始值分析延续方法，用于给定的数据，这些函数旨在适应性地工作。 。
This paper wants to increase our understanding and computational know-how for time--varying matrix problems and Zhang Neural Networks (ZNNs). These neural networks were invented for time or single parameter--varying matrix problems around 2001 in China and almost all of their advances have been made in and most still come from its birthplace. Zhang Neural Network methods have become a backbone for solving discretized sensor driven time--varying matrix problems in real-time, in theory and in on--chip applications for robots, in control theory and other engineering applications in China. They have become the method of choice for many time--varying matrix problems that benefit from or require efficient, accurate and predictive real--time computations. A typical discretized Zhang Neural Network algorithm needs seven distinct steps in its initial set-up. The construction of discretized Zhang Neural Network algorithms starts from a model equation with its associated error equation and the stipulation that the error function decrease exponentially fast. The error function differential equation is then mated with a convergent look-ahead finite difference formula to create a distinctly new multi--step style solver that predicts the future state of the system reliably from current and earlier state and solution data. Matlab codes of discretized Zhang Neural Network algorithms for time varying matrix problems typically consist of one linear equations solve and one recursion of already available data per time step. This makes discretized Zhang Neural network based algorithms highly competitive with ordinary differential equation initial value analytic continuation methods for function given data that are designed to work adaptively. .
