Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks
Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks
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DOI：
10.1109/tnn.2008.2003250
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发表时间：
2008-11
影响因子：
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通讯作者：
Jinling Liang;Zidong Wang;Yurong Liu;Xiao-Han Liu
中科院分区：
文献类型：
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作者：
Jinling Liang;Zidong Wang;Yurong Liu;Xiao-Han Liu
研究了一类具有时变时滞的耦合随机离散时间神经网络的鲁棒同步问题。单个神经网络受到参数不确定性、随机扰动和时变时滞的影响，其中状态矩阵和权值矩阵中都存在范数有界的参数不确定性，随机扰动以标量Wiener过程的形式存在，时滞进入激活函数。对于耦合神经网络阵列，同时考虑了常耦合和时滞耦合。我们的目标是建立易于验证的条件，在该条件下寻址的神经网络是同步的。利用Kronecker积作为一种有效的工具，发展了线性矩阵不等式(LMI)方法，得到了耦合时滞神经网络在均方意义下全局、鲁棒、指数同步的几个充分判据。所得到的基于LMI的条件不仅依赖于时变时滞的下界，而且还依赖于时变时滞的上界，并且可以通过MatLab的LMI工具箱有效地求解。文中给出了两个数值例子，验证了所提出的同步方案的有效性。
This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme.