School of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China; School of Education, Xizang Minzu University, Xianyang 712082, China.
School of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
Neural Netw. 2017 Jun;90:42-55. doi: 10.1016/j.neunet.2017.03.006. Epub 2017 Mar 23.
This paper is concerned with the fixed-time synchronization for a class of complex-valued neural networks in the presence of discontinuous activation functions and parameter uncertainties. Fixed-time synchronization not only claims that the considered master-slave system realizes synchronization within a finite time segment, but also requires a uniform upper bound for such time intervals for all initial synchronization errors. To accomplish the target of fixed-time synchronization, a novel feedback control procedure is designed for the slave neural networks. By means of the Filippov discontinuity theories and Lyapunov stability theories, some sufficient conditions are established for the selection of control parameters to guarantee synchronization within a fixed time, while an upper bound of the settling time is acquired as well, which allows to be modulated to predefined values independently on initial conditions. Additionally, criteria of modified controller for assurance of fixed-time anti-synchronization are also derived for the same system. An example is included to illustrate the proposed methodologies.
本文研究了一类含有不连续激活函数和参数不确定性的复值神经网络的固定时间同步问题。固定时间同步不仅要求主从系统在有限时间片段内实现同步，而且要求所有初始同步误差的时间间隔有一个统一的上界。为了实现固定时间同步的目标，为从神经网络设计了一种新的反馈控制程序。通过 Filippov 不连续理论和 Lyapunov 稳定性理论，为控制参数的选择建立了一些充分条件，以保证在固定时间内实现同步，同时获得了 settling time 的上界，该上界可以根据初始条件独立地调制到预定义的值。此外，还为同一系统推导了固定时间反同步的修正控制器的准则。通过一个例子来说明所提出的方法。
