基于忆阻时滞神经网络的耗散研究

发布时间：2018-10-31 13:34

【摘要】：针对一类基于忆阻时滞神经网络的耗散问题,提出一种结合倒凸技术和Wirtinger积分不等式的耗散方法。首先,应用微分包含和集值映射理论,将忆阻时滞神经网络转化成传统的时滞神经网络;接着,构造含有时滞系数的状态向量2次项和3重积分项的Lyapunov-Krasovskii泛函(LKF),应用倒凸技术和Wirtinger积分不等式估计LKF微分,得到了确保时滞神经网络严格耗散的时滞依赖条件,这些条件可以用线性矩阵不等式形式表示并且易于用Matlab软件实现。将该方法推广到研究时滞神经网络无缘分析问题中。在数值例子中,针对不同的时滞变化率上界,与现有文献的最优耗散性能指标进行比较,实验结果表明,本文方法将其提高了5%。另外,在相同时滞条件下,仿真分别给出了神经网络系统有外部输入和无外部输入的状态轨迹,由仿真结果可以看出外部输入的存在的确破坏系统稳定性。
[Abstract]:For a class of dissipative problems based on memory delay neural networks, a dissipative method combining inverse convex technique and Wirtinger integral inequality is proposed. Firstly, by using the theory of differential inclusion and set-valued mapping, the neural network with memory delay is transformed into a traditional neural network with time-delay. Then, the Lyapunov-Krasovskii functional (LKF), with two and three multiple integral terms of state vector with time-delay coefficients is constructed to estimate the LKF differential by using backward convex technique and Wirtinger integral inequality, and the time-delay dependent conditions to ensure strict dissipation of delayed neural networks are obtained. These conditions can be expressed in the form of linear matrix inequalities and are easily realized by Matlab software. This method is extended to the study of neural networks with time delay. In numerical examples, for different upper bounds of time-delay change rate, compared with the optimal dissipative performance index of existing literature, the experimental results show that the proposed method improves the efficiency of the proposed method by 5%. In addition, under the same time-delay condition, the state trajectories of the neural network system with and without external inputs are given, respectively. From the simulation results, it can be seen that the existence of external inputs does damage to the stability of the system.
【作者单位】：西安电子科技大学机电工程学院;咸阳师范学院数学与信息科学学院;
【基金】：国家自然科学基金资助项目(61673310;61501388;11501482)
【分类号】：TP183

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