参数扰动下时滞忆阻神经网络的Lagrange稳定性  

Lagrange stability of delayed memristive neural networks with parameter perturbations

作　　者：李梁晨 甘勤涛 蔺佳哲 Li Liangchen;Gan Qintao;Lin Jiazhe(Army Engineering University Shijiazhuang Campus,Shijiazhuang 050003,China;National Key Laboratory of Blind Signal Processing,Chengdu 610000,China;Computational Aerodynamics Research Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]陆军工程大学石家庄校区,石家庄050000 [2]盲信号处理国家级重点实验室,成都610000 [3]中国空气动力研究与发展中心计算空气动力研究所,绵阳621000

出　　处：《东南大学学报（自然科学版）》2021年第3期511-520,共10页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11871316,11371368).

摘　　要：根据忆阻器物理特性,建立了一类荷控忆阻神经网络模型,模型中忆阻器的记忆特性被保留.针对实际忆阻器阻值与理想模型存在差异造成忆阻神经网络中参数不确定的问题,研究参数扰动下时滞忆阻神经网络的Lagrange稳定性.将模型重构为双重扰动形式以处理忆阻器忆阻值变化造成的模型中的参数变化.通过构造Lyapunov函数和应用线性矩阵不等式方法,以线性矩阵不等式形式给出了网络Lagrange稳定的充分条件,并给出了相应的全局指数吸引集的估计.最后,通过与现有模型的仿真结果对比,展示了所建立模型的优势.利用数值算例展示了参数扰动造成忆阻神经网络周期解的偏移,说明了研究参数扰动对忆阻神经网络稳定性影响的必要性,并验证了理论所得稳定性判据的可行性.Based on the physical property of memristors,a kind of charge controlled memristive neural network model is established.Considering the effects of parameter uncertainties caused by the difference between the actual memristance and the ideal model,the Lagrange stability of the delayed memristive neural network with parameter perturbations is investigated.To handle the parameters variety in the model,the model is reconstructed to a form with double parameter perturbations.By using Lyapunov functions and linear matrix inequality technique,a sufficient condition is given to ascertain the network to be stable in Lagrange sense.Meanwhile,the estimation of the corresponding globally attractive set is given.Compared with the simulation results of the existing models,the advantages of the proposed model are illustrated.Also,a numerical example reveals the shift of the periodic solution of the memristive neural network caused by parameter perturbations,which shows the necessity of studying the effects of parameter perturbations on the stability of the memristive neural network,and the feasibility of the stability criterion obtained is verified.

关 键 词：忆阻神经网络 LAGRANGE稳定性 参数扰动 线性矩阵不等式 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]