IEEE Trans Cybern. 2021 Jun;51(6):3212-3223. doi: 10.1109/TCYB.2020.2980684. Epub 2021 May 18.
This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.
本文主要关注完全复变量时滞神经网络在不将原始复变量神经网络分为两个实域子系统的情况下，在有限和固定时间内的同步问题，涉及不连续激活和时变时滞。为了避免分离方法，提出了复值符号函数，并建立了其性质。通过引入的符号函数，在二次范数和基于实部和虚部绝对值的新范数下，开发了两种不连续控制策略。通过在复域中应用非光滑分析和一些新的不等式技术，得出了几个同步准则和 settling time 的估计。特别是，在新的范数框架下，设计了一个统一的控制策略，并揭示了控制器中的一个参数值完全决定了网络是否在有限时间或固定时间内同步。最后，提供了一个例子的数值结果，以支持所建立的理论结果。
