本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Ra...本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.展开更多
本文研究带有时延的分数阶复值惯性神经网络的有限时间控制问题。首先使用变量代换法将高阶复值系统转化为四个低阶实值系统,然后根据新提出的有限时间稳定性引理,构造李亚普洛夫函数,使得驱动和响应系统可以在设计的非线性控制器下达...本文研究带有时延的分数阶复值惯性神经网络的有限时间控制问题。首先使用变量代换法将高阶复值系统转化为四个低阶实值系统,然后根据新提出的有限时间稳定性引理,构造李亚普洛夫函数,使得驱动和响应系统可以在设计的非线性控制器下达到同步且得到其沉降时间。最后,给出一个数值仿真去检验得到的理论结果的正确性。This paper studies the finite-time control problem of time-delayed fractional-order complex-valued inertial neural networks. Firstly, the higher-order complex-valued system is converted into four lower-order real-valued systems using the variable substitution method. Then, based on the newly proposed finite-time stability lemma, a Lyapunov function is constructed and a nonlinear controller is designed to guarantee that the response system can be synchronized to the drive system in finite time and that the settling time is derived simultaneously. Finally, a numerical example is given to check the correctness of the theoretical results.展开更多
基金Supported by the National Natural Science Foundation of China(11371368,11071254,61305076)the Natural Science Foundation of Hebei Province of China(A2014506015)
文摘本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.
文摘本文研究带有时延的分数阶复值惯性神经网络的有限时间控制问题。首先使用变量代换法将高阶复值系统转化为四个低阶实值系统,然后根据新提出的有限时间稳定性引理,构造李亚普洛夫函数,使得驱动和响应系统可以在设计的非线性控制器下达到同步且得到其沉降时间。最后,给出一个数值仿真去检验得到的理论结果的正确性。This paper studies the finite-time control problem of time-delayed fractional-order complex-valued inertial neural networks. Firstly, the higher-order complex-valued system is converted into four lower-order real-valued systems using the variable substitution method. Then, based on the newly proposed finite-time stability lemma, a Lyapunov function is constructed and a nonlinear controller is designed to guarantee that the response system can be synchronized to the drive system in finite time and that the settling time is derived simultaneously. Finally, a numerical example is given to check the correctness of the theoretical results.
