基于有限时间神经网络求解的时变复数矩阵方程  

Solving time-varying complex matrix equations based on finite-time neural network

作　　者：高畅 孔颖[1] 胡汤珑 GAO Chang;KONG Ying;HU Tanglong(School of Information and Eletronic Engineering,Zhejiang University of Science and Technology,Hangzhou 310023,Zhejiang,China)

机构地区：[1]浙江科技学院信息与电子工程学院,杭州310023

出　　处：《浙江科技学院学报》2022年第5期409-418,共10页Journal of Zhejiang University of Science and Technology

基　　金：国家自然科学基金项目(61803338)。

摘　　要：为求解时变复数矩阵方程,根据复数域中两种等价处理非线性激励函数的方法,提出了两种新型有限时间归零神经网络(new finite-time zeroing neural network,NFTZNN)模型。尝试将一种新型激励函数应用到两种NFTZNN模型中,从而提高了模型的综合性能。试验结果表明,与现有的复数神经网络(complex-value zeroing netural network,CVZNN)模型相比,使用新型激励函数的NFTZNN模型在求解时变复数矩阵方程时,收敛速度更快、计算精度更高;并且,根据李亚普洛夫定理计算出的收敛时间上界也更接近实际的收敛时间。本研究提出的神经网络模型能准确快速地求解出复数域中的时变矩阵方程,可以为后续工程应用提供参考。Aiming at solving the time-varying complex matrix equations,two new finite-time zeroing neural network(NFTZNN)models were proposed according to two equivalent methods to deal with nonlinear activation functions in the complex domain.A new activation function was applied to two NFTZNN models to improve the comprehensive performance of the models.The experimental results show that compared with the existing complex-value zeroing neural network(CVZNN)model,the NFTZNN models using the new activation function boast faster convergence speed and higher calculation accuracy when solving time-varying complex matrix equations.Moreover,the upper bound of the convergence time calculated according to the Lyapunov theorem is also closer to the actual convergence time.The proposed neural network models can accurately and quickly solve the time-varying matrix equations in the complex field,which can provide important reference for subsequent engineering applications.

关 键 词：矩阵方程 有限时间归零神经网络 新型激励函数 收敛时间上界 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]