This paper investigates the synchronization of multiple memristive neural networks (MMNNs) under cyber-physical attacks through distributed event-triggered control. In the field of multi-agent dynamics, memristive neural network (MNN) is considered as a kind of switched systems because of its state-dependent parameters which can lead to the parameters mismatch during synchronization. This will increase the uncertainty of the system and affect the theoretical analysis. Also, neural network is considered as a typical nonlinear system. Therefore, the model studied in this paper is a nonlinear system with switching characteristics. In complex environments, MMNNs may receive mixed attacks, one of which is called cyber-physical attacks that may influence both communication links and MNN nodes to cause changes in topology and physical state. To tackle this issue, we construct a novel Lyapunov functional and use properties of M-matrix to get the criteria for synchronization of MMNNs under cyber-physical attacks. It is worth mentioning that the controllers in this paper are designed to be distributed under event-triggering conditions and Zeno behavior is also excluded. In addition, the algorithm of parameter selection is given to help designing the controllers. One example is given at the end of the paper to support our results.

本文研究了通过分布式事件触发控制在网络物理攻击下的多个忆阻神经网络（MMNN）的同步。在多智能体动力学领域，忆阻神经网络（MNN）被认为是一种交换系统，因为它的状态相关参数会导致同步期间的参数不匹配。这将增加系统的不确定性并影响理论分析。而且，神经网络被认为是典型的非线性系统。因此，本文研究的模型是具有切换特性的非线性系统。在复杂的环境中，MMNN可能会受到混合攻击，其中一种被称为网络物理攻击，可能会影响通信链路和MNN节点，从而导致拓扑和物理状态发生变化。M-矩阵可获取在网络物理攻击下MMNN同步的标准。值得一提的是，本文中的控制器被设计为在事件触发条件下进行分布，并且不包括Zeno行为。另外，给出了参数选择算法以帮助设计控制器。本文结尾给出了一个例子来支持我们的结果。