基于变参的零化神经网络算法求解复值动态线性矩阵方程

Solving Complex-Valued Time-Varying Linear Matrix Equations Based on the Annihilating Neural Network Algorithm with Variable Parameters

摘要: 动态复值线性矩阵方程的求解是数学和控制理论中频繁出现的问题，零化神经网络算法作为求解线性矩阵方程的有效方法受到众多学者关注，从而衍生出许多零化神经网络算法的变形。但已有的大多数文献中所设计的模型采用的为固定参数，本文构建了时变参数的零化神经网络算法，通过构建精巧的时变参数和激活函数的设计，在没有效率损失的情况下，较大地提升了算法的收敛速度，并增强了抗噪性，论文最后通过数值实验验证了理论分析。

Abstract: Solving time-varying complex-valued linear matrix equations is a frequently encountered problem in mathematics and control theory. The annihilating neural network algorithm, as an effective method for solving linear matrix equations, has attracted the attention of many scholars, leading to the emergence of many variants of this algorithm. However, most of the existing models designed in the literature use fixed parameters. In this paper, an annihilating neural network algorithm with time-varying parameters is constructed. Through the delicate design of time-varying parameters and activation functions, the convergence speed of the algorithm is significantly improved without sacrificing efficiency, and the noise resistance is enhanced. Finally, numerical experiments are conducted to verify the theoretical analysis.