基于时滞观测的神经网络的随机镇定Stochastic stabilization of neural networks based on time-delay observation
李树德,时正华,何秀丽
摘要(Abstract)：
研究神经网络的随机镇定问题.通过在扩散项中加入含时滞项的状态控制,利用随机稳定性理论,镇定一类循环神经网络.同时,利用It公式及多种不等式性质,证明解的几乎必然指数稳定性,并给出数值例子.
关键词(KeyWords)： 神经网络;时滞;随机镇定;It积分
基金项目(Foundation): 中央高校基本科研业务费专项基金(2018B19914)资助
作者(Author): 李树德,时正华,何秀丽
参考文献(References)：
- [1]Krizhevsky A,Sutskever I,Hinton G. Imagenet classification with deep convolutional neural networks[Z]. In NIPS,2012,60(2):1097-1105.
- [2]Lecun Y,Bottou L,Orr G,et al. Efficient backprop[J]. In Neural Networks:Tricks of the Trade,1998,1524(1):9-50.
- [3]Jin K,Mccann M,Froustey E,et al. Deep convolutional neural network for inverse problems in imaging[J]. IEEE Trans Image Process,2017,26(9):4509-4522.
- [4]Zhang T,Qi G,Xiao B,et al. Interleaved group convolutions for deep neural networks[C]. In International Conferenceon Computer Vision,2017.
- [5]Huang H,Cao J. Exponential stability analysis of uncertain stochastic neural networks with multipledelays[J]. Nonlinear Anal:Real World Appl,2007,8(2):646-653.
- [6]Blythe S,Mao X,Liao X. Stability of stochastic delay neuralnetworks[J]. J Franklin Inst,2001,338:481-495.
- [7]Song Q,Wang Z. Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays[J].Physica A Statistical Mechanics&Its Applications,2012,387(13):3314-3326.
- [8]He Y,Liu P G,Rees D,et al. Stability analysis for neural networks with time-varying intervaldelay[J]. IEEE Trans Neural Netw,2007,18(6):1850-1854.
- [9]黄礼荣,邓飞其,宋明辉.随机镇定与反镇定概述[J].南京信息工程大学学报,2017,9(3):262-273.
- [10]Luo W,Zhong K,Zhu S,et al. Further results on robustness analysis of global exponential stability of recurrent neural networks with time delays and random disturbances[J]. Neural Networks,2014,53(5):127-133.
- [11]Zhu S,Yang Q,Shen Y. Noise further expresses exponential decay for globally exponentially stable time-varying delayed neural networks[J]. Elsevier Science Ltd,2016,77(C):7-13.
- [12]Mao X. Almost sure exponential stabilization by discrete-time stochastic feedbackcontrol[J]. IEEE Trans Automat Control,2016,61(6):1619-1624.
- [13]Guo Q,Mao X,Yue R. Almost sure exponential stability of stochaostic differential delay equations[J]. SIAM J Control Optim,2016,54:1919-1933.
- [14] Shen Y,Wang J. Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and markovian-switching parameters[J]. IEEE Trans Neural Netw,2007,18(6):1857-1862.
- [15]Mao X. Stochastic differential equations and their applications[M]. 2nded. Elsevier,2007.