摘要
针对传统的四元数乘法运算不满足交换律的问题,介绍了一种可交换四元数,同时建立一种交换四元数神经网络(CQVNN),并对CQVNN的渐近稳定性进行研究。研究过程中,将CQVNN分解成4个实值神经网络,通过拓扑度理论、传统的李雅普诺夫稳定性理论以及不等式理论,得到CQVNN平衡点的存在唯一性条件以及其平衡点渐近稳定的充分条件。最后,给出一个数值案例,以验证所得结论的有效性。
Because the traditional quaternion multiplication does not meet the commutative law,a kind of commutative quaternion was introduced,and a commutative quaternion valued neural network(CQVNN)was established,and the asymptotic stability of the CQVNN was studied.In the course of research,the CQVNN were decomposed into four real-valued neural networks.Then,through the topological degree theory,the traditional Lyapunov stability theory and the inequality theory,the conditions for the existence and uniqueness of the equilibrium point of CQVNN and the linear matrix inequality(LMI)conditions for the asymptotically stable of equilibrium point were obtained.Finally,a numerical example was given to verify the validity of the conclusion.
作者
林东源
陈晓丰
孙文涛
李伟凯
夏砚楠
LIN Dongyuan;CHEN Xiaofeng;SUN Wentao;LI Weikai;XIA Yannan(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China;School of Science,Tibet University,Lhasa 850000,China;College of Computer Science&Technology,Nanjing University of Aeronautics&Astronautics,Nanjing 210016,China)
出处
《智能科学与技术学报》
2020年第1期80-87,共8页
Chinese Journal of Intelligent Science and Technology
基金
重庆市自然科学基金资助项目(No.cstc2018jcyjAX0606,No.cstc2017jcyjAX0082)
重庆市教育委员会科学技术研究基金资助项目(No.KJQN201900701)。
关键词
交换四元数
时滞神经网络
渐近稳定性
commutative quaternion
delayed neural network
asymptotically stability
