College of Science, Wuhan University of Science and Technology, Wuhan 430065, China; Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China.
School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
Neural Netw. 2023 Jun;163:53-63. doi: 10.1016/j.neunet.2023.03.031. Epub 2023 Mar 27.
The synchronization problem of bidirectional associative memory memristive neural networks (BAMMNNs) with time-varying delays plays an essential role in the implementation and application of neural networks. Firstly, under the framework of the Filippov's solution, the discontinuous parameters of the state-dependent switching are transformed by convex analysis method, which is different from most previous approaches. Secondly, based on Lyapunov function and some inequality techniques, several conditions for the fixed-time synchronization (FXTS) of the drive-response systems are obtained by designing special control strategies. Moreover, the settling time (ST) is estimated by the improved fixed-time stability lemma. Thirdly, the driven-response BAMMNNs are investigated to be synchronized within a prescribed time by designing new controllers based on the FXTS results, where ST is irrelevant to the initial values of BAMMNNs and the parameters of controllers. Finally, a numerical simulation is exhibited to verify the correctness of the conclusions.
双向联想记忆人工神经网络 (BAMMNN) 的时变时滞同步问题在神经网络的实现和应用中起着至关重要的作用。首先，在 Filippov 解的框架下，通过凸分析方法将状态相关切换的不连续参数进行转换，这与大多数先前的方法不同。其次，基于 Lyapunov 函数和一些不等式技术，通过设计特殊的控制策略，获得了驱动-响应系统固定时间同步 (FXTS) 的几个条件。此外，通过改进的固定时间稳定性引理来估计settling time (ST)。第三，基于 FXTS 结果，通过设计新的控制器，研究了驱动-响应 BAMMNN 在规定时间内的同步问题，其中 ST 与 BAMMNN 的初始值和控制器的参数无关。最后，展示了一个数值模拟来验证结论的正确性。
