College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China.
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China.
Neural Netw. 2023 Jul;164:497-507. doi: 10.1016/j.neunet.2023.05.005. Epub 2023 May 8.
This paper presents new theoretical results on quasi-projective synchronization (Q-PS) and complete synchronization (CS) of one kind of discrete-time fractional-order delayed neural networks (DFDNNs). At first, three new fractional difference inequalities for exploring the upper bound of quasi-synchronization error and adaptive synchronization are established by dint of Laplace transform and properties of discrete Mittag-Leffler function, which vastly expand a number of available results. Furthermore, two controllers are designed including nonlinear controller and adaptive controller. And on the basis of Lyapunov method, the aforementioned inequalities and properties of fractional-order difference operators, some sufficient synchronization criteria of DFDNNs are derived. Because of the above controllers, synchronization criteria in this paper are less conservative. At last, numerical examples are carried out to illustrate the usefulness of theoretical upshots.
本文提出了离散时间分数阶时滞神经网络（DFDNN）一类的准投影同步（Q-PS）和完全同步（CS）的新理论结果。首先，通过拉普拉斯变换和离散 Mittag-Leffler 函数的性质，建立了三个新的分数差分不等式，以探索准同步误差和自适应同步的上界，极大地扩展了一些可用的结果。此外，设计了两个控制器，包括非线性控制器和自适应控制器。并且，基于 Lyapunov 方法，上述不等式和分数阶差分算子的性质，得出了 DFDNN 的一些充分同步准则。由于有了上述控制器，本文中的同步准则不太保守。最后，通过数值例子说明了理论结果的有效性。
