有限时间网络求解时变复矩阵的逆及抗噪声分析  

Finite-time neural network for solving time-varying complex matrix inversion and anti-noise analysis

作　　者：苗鹏[1] 李鑫 MIAO Peng;LI Xin(Department of Basic Courses,Zhengzhou University of Science and Technology,Zhengzhou 450064,Henan,China;Business School,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]郑州科技学院基础部,河南郑州450064 [2]西北师范大学商学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2023年第6期22-29,共8页Journal of Northwest Normal University(Natural Science)

基　　金：河南省高校重点科研项目(21B110008);郑州科技学院优秀青年教师基金资助项目(80000320018);甘肃省高等学校创新基金项目(2022A-005);西北师范大学青年教师科研能力提升项目(NWNU-SKQN2022-34)。

摘　　要：设计了一个特殊的带有可调激活函数的有限时间递归神经网络求解时变复数矩阵的逆,同时分析了其抗噪声能力.首先,时变复数矩阵逆问题被转化为一个误差矩阵,为了使此误差矩阵收敛到零,提出了一个带有可调激活函数的有限时间递归神经网络,并在此基础上设计了一个带有噪声干扰项的网络;其次,证明了设计网路的有限时间稳定性并估计了收敛时间上界,证明了添加噪声干扰项后的网络误差可以收敛到零;最后,通过两个数值例子展现了方法的有效性、优越性和设计网络在添加多种形式噪声时的强鲁棒性.In this paper,a special finite time recurrent neural network with adjustable activation function is designed to solve the time-varying complex matrix inversion,and its anti-noise ability is analyzed.First,the time-varying complex matrix inversion problem is transformed into a time-varying complex error matrix.In order to make the error matrix converge to zero,a finite time recurrent neural network with adjustable activation function is proposed,and a network with noise interference term is designed based on this network.Then,the finite time stability of the designed network is proved and the upper bound of the convergence time is estimated.Finally,two numerical examples are given to demonstrate the effectiveness and superiority of the proposed method,and the strong robustness of the designed network is also discussed when adding various forms of noise.

关 键 词：复矩阵逆 递归神经网络 噪声干扰 有限时间稳定性 鲁棒性 

分 类 号：O175.13[理学—数学] TN957.54[理学—基础数学]