Passivity Analysis for Memristor-Based Inertial Neural Networks With Discrete and Distributed Delays
Passivity Analysis for Memristor-Based Inertial Neural Networks With Discrete and Distributed Delays
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DOI：
10.1109/tsmc.2017.2732503
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发表时间：
2019-02
期刊：
影响因子：
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通讯作者：
Qiang Xiao;Zhenkun Huang;Z. Zeng
中科院分区：
文献类型：
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作者：
Qiang Xiao;Zhenkun Huang;Z. Zeng
已有的神经网络无源性的研究成果主要集中在状态的一阶导数上，而研究具有高阶导数的无源性也具有重要意义。本文研究了一类具有外部输入和输出的基于忆阻器的惯性神经网络。首先，通过选择适当的变量变换，将原网络改写为一阶微分方程组。然后利用非光滑分析和线性矩阵不等式(LMI)技术给出了MinN的无源性判据，该判据也可能导致NP-Hard问题，因为它至少需要指数时间来求解无源性条件。同时，基于所得到的无源性判据，给出了Minns的渐近稳定性判据。为了避免NP-Hard问题，我们使用了矩阵分析技术，其性质是给定的矩阵和所提出的矩阵之间的差阵是半负定的。然后，将所提出的无源性判据的时间复杂度降低为关于线性矩阵不等式个数的恒定时间。对于有界的不确定参数，还研究了Minns的鲁棒无源性。Minn拓宽了神经网络设计的应用范围。最后给出了相关的仿真算例，验证了所得结果的有效性。
The existing results of passivity for neural networks mainly concentrated on first-order derivative of the states, whereas it is also significant to study the passivity with high-order derivative. In this paper, a class of memristor-based inertial neural networks (MINNs) with external inputs and outputs are concerned. First, by choosing appropriate variable transformation, the original networks are rewritten as first-order differential equations. Then a criterion of passivity for the MINNs is presented by nonsmooth analysis and linear matrix inequality (LMI) techniques, which could also result in NP-hard problem since it needs at least exponential-time to solve the passivity condition. Meanwhile, based on the obtained passivity criterion, asymptotic stability criterion is accordingly derived for MINNs. In order to avoid the NP-hard problem, we employ matrix-analysis-techniques with the property that the difference-matrix between the given matrix and the proposed matrix is seminegative definite. Then the time complexity for solving the proposed passivity criterion is reduced to constant-time with respect to the number of LMIs. Robust passivity for MINNs is also studied for bounded uncertain parameters. The MINN widens the application ranges for designing neural networks. Finally, relevant simulation examples are given to show the effectiveness of the obtained results.