四元数双向联想记忆神经网络的固定时间控制  

Fixed-time synchronization of quaternion-valued BAM neural networks

作　　者：石雨晨 魏若宇 SHI Yuchen;WEI Ruoyu(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China;Center for Applied Mathematics of Jiangsu Province,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044 [2]南京信息工程大学江苏省应用数学中心,江苏南京210044

出　　处：《南通大学学报（自然科学版）》2023年第3期81-94,共14页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金青年科学基金项目(12301652);江苏省基础研究计划青年基金项目(BK20210635);省级大学生创新创业训练计划项目(202210300128Y)。

摘　　要：将双向联想记忆(bidirectional associative memory,BAM)神经网络扩展到四元数域,提出了一类新的四元数双向联想记忆神经网络(quaternion-valued bidirectional associative memory neural networks,QVBAMNNs)。通过对四元数的分解并运用微分包含理论,将原始的四元数值系统转化为等价的实值系统,并利用Lyapunov方法研究了主从QVBAMNNs的固定时间同步问题。通过设计一个不连续状态反馈控制器,得到了保证QVBAMNNs达到固定时间同步的新准则。最后,通过数值仿真验证了所得结果的正确性。The bidirectional associative memory(BAM)neural networks is extended to the quaternion domain and a new type of quaternion-valued bidirectional associative memory neural networks(QVBAMNNs)is proposed.By decomposing quaternions and applying differential inclusion theory,the original quaternion-valued system is transformed into an equivalent real-valued system.The fixed-time synchronization problem between the master and slave QVBAMNNs is studied using Lyapunov′s method.By designing a discontinuous state feedback controller,a new criterion guaranteeing the fixed-time synchronization of QVBAMNNs is obtained.Finally,the correctness of the obtained results is verified through numerical simulations.

关 键 词：固定时间同步 四元数 不连续激活函数 双向联想记忆神经网络 微分包含 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]