IEEE Trans Neural Netw Learn Syst. 2022 Oct;33(10):5542-5556. doi: 10.1109/TNNLS.2021.3070966. Epub 2022 Oct 5.
This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.
本文针对忆阻复值神经网络（MCVNN）在固定时间或预定时间内的同步问题进行了研究，其中状态变量、激活函数、神经元自抑制率、神经元连接忆阻权重和外部输入均被假设为复数值。首先，利用比较原理系统地建立了更全面的固定时间稳定性定理和更精确的稳定时间（ST）估计。其次，通过引入复数的不同范数，而不是将复值系统分解为实部和虚部，我们成功地设计了几个更简单的不连续控制器，获得了改进的固定时间同步（FXTS）结果。第三，基于类似的数学推导，通过新开发的控制策略探讨了预定时间同步（PATS）条件，其中 ST 可以预先指定，且与神经网络和控制器的初始值以及任何参数无关。最后，通过数值模拟验证了改进的同步方法的有效性和优越性。
