Zhang Hao, Zhou Yufeng, Zeng Zhigang
IEEE Trans Cybern. 2023 May;53(5):3277-3287. doi: 10.1109/TCYB.2022.3168090. Epub 2023 Apr 21.
Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω -type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω -type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.
近年来，对具有自适应控制器的两个时滞神经网络的主从同步进行了研究；然而，网络模型中现有的时滞是有界的或无界的，并带有一些导数约束。对于没有这些限制的更一般的时滞，如何设计合适的自适应控制器并严格证明误差系统的收敛性仍然是一个具有挑战性的问题。本文对此问题给出了肯定的答案。借助无界时滞系统的稳定性结果和一些分析技巧，我们证明即使网络时滞无界且没有任何导数约束，传统的集中式自适应算法也能实现全局渐近同步。为了描述同步误差的收敛速度，还提供了依赖于灵活的ω型函数的自适应设计来控制同步误差，这可以导致指数同步、多项式同步和对数同步。给出了时滞神经网络和类混沌池田振子的数值例子来验证自适应设计，并且我们发现，在无界时滞的情况下，ω型函数的介入可以促进同步的实现，但可能会破坏控制增益的收敛性，而在有界时滞的情况下则不会出现这种情况。
