基于离散时间观测的神经网络的随机镇定
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摘要
主要讨论了离散时间观测下的神经网络的随机镇定.首先,通过使用伊藤公式、Gronwall不等式、Burkholder-Davis-Gandy不等式等,证明得到离散时间观测的神经网络随机镇定的条件.其次,利用数值例子来对结论加以证明.
The stochastic stabilization of neural networks under discrete-time observations is discussed. First,by using the Ito formula,the Gronwall inequality,Burkholder-Davis-Gandy inequality,the conditions of stochastic stabilization of neural networks based on discrete-time observations are proved. Finally,a numerical example is used to illustrate the conclusion.
The stochastic stabilization of neural networks under discrete-time observations is discussed. First,by using the Ito formula,the Gronwall inequality,Burkholder-Davis-Gandy inequality,the conditions of stochastic stabilization of neural networks based on discrete-time observations are proved. Finally,a numerical example is used to illustrate the conclusion.
引文
[1] SONG Q,CAO J. Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses[J].Journal of the Franklin Institute,2008,345(1):39-59.
[2]CAO J. Periodic oscillation and exponential stability of delayed CNNs[J]. Physics Letters A,2000,270(3/4):157-163.
[3]LU W,CHEN T. Dynamical behaviors of Cohen–Grossberg neural networks with discontinuous activation functions[J]. Neural Networks,2005,18(3):231-242.
[4]CARABALLO T,LIU K,MAO X. On stabilization of partial differential equations by noise[J]. Nagoya Mathematical Journal,2001,161:155-170.
[5]ZHU S,SHEN Y,CHEN G. Noise suppress or express exponential growth for hybrid Hopfield neural networks[J]. Physics letters A,2010,374(19/20):2035-2043.
[6]APPLEBY J A D,MAO X,RODKINA A. Stabilisation and destabilisation of nonlinear differential equations by noise[J]. IEEE Transactions on Automatic Control,2008,53(3):683-691.
[7]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(自然科学版),2017,9(3):262-273.
[8]BLYTHE S,MAO X,LIAO X. Stability of stochastic delay neural networks[J]. Journal of the Franklin Institute,2001,338(4):481-495.
[9]SUN Y,CAO J. Stabilization of stochastic delayed neural networks with Markovian switching[J]. Asian Journal of Control,2008,10(3):327-340.
[10]LI X,CAO J. Exponential stability of stochastic cohen-grossberg neural networks with time-varying delays[C]//International Symposium on Neural Networks. Berlin:Springer,2005:162-167.
[11]LIU Y,WANG Z,LIU X. State estimation for discrete-time neural networks with markov-mode-dependent lower and upper bounds on the distributed delays[J]. Neural processing letters,2012,36(1):1-19.
[12]WANG Z,WANG Y,LIU Y. Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays[J]. IEEE transactions on neural networks,2010,21(1):11-25.
[13]MAO X. Almost sure exponential stabilization by discrete-time stochastic feedback control[J]. IEEE Transactions on Automatic Control,2016,61(6):1619-1624.
[14]DENG F,LUO Q,MAO X. Stochastic stabilization of hybrid differential equations[J]. Automatica,2012,48(9):2321-2328.
[15]MAO X. Stochastic Differential Equations and Applications[M]. 2nd Edition. Horwood:Chichester,2007:51-55.
[2]CAO J. Periodic oscillation and exponential stability of delayed CNNs[J]. Physics Letters A,2000,270(3/4):157-163.
[3]LU W,CHEN T. Dynamical behaviors of Cohen–Grossberg neural networks with discontinuous activation functions[J]. Neural Networks,2005,18(3):231-242.
[4]CARABALLO T,LIU K,MAO X. On stabilization of partial differential equations by noise[J]. Nagoya Mathematical Journal,2001,161:155-170.
[5]ZHU S,SHEN Y,CHEN G. Noise suppress or express exponential growth for hybrid Hopfield neural networks[J]. Physics letters A,2010,374(19/20):2035-2043.
[6]APPLEBY J A D,MAO X,RODKINA A. Stabilisation and destabilisation of nonlinear differential equations by noise[J]. IEEE Transactions on Automatic Control,2008,53(3):683-691.
[7]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(自然科学版),2017,9(3):262-273.
[8]BLYTHE S,MAO X,LIAO X. Stability of stochastic delay neural networks[J]. Journal of the Franklin Institute,2001,338(4):481-495.
[9]SUN Y,CAO J. Stabilization of stochastic delayed neural networks with Markovian switching[J]. Asian Journal of Control,2008,10(3):327-340.
[10]LI X,CAO J. Exponential stability of stochastic cohen-grossberg neural networks with time-varying delays[C]//International Symposium on Neural Networks. Berlin:Springer,2005:162-167.
[11]LIU Y,WANG Z,LIU X. State estimation for discrete-time neural networks with markov-mode-dependent lower and upper bounds on the distributed delays[J]. Neural processing letters,2012,36(1):1-19.
[12]WANG Z,WANG Y,LIU Y. Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays[J]. IEEE transactions on neural networks,2010,21(1):11-25.
[13]MAO X. Almost sure exponential stabilization by discrete-time stochastic feedback control[J]. IEEE Transactions on Automatic Control,2016,61(6):1619-1624.
[14]DENG F,LUO Q,MAO X. Stochastic stabilization of hybrid differential equations[J]. Automatica,2012,48(9):2321-2328.
[15]MAO X. Stochastic Differential Equations and Applications[M]. 2nd Edition. Horwood:Chichester,2007:51-55.