In this paper, a novel memristive neural networks model is developed. In the new model, the states of memristors are related to the initial resistance of the memristors and the amount of charge flowing through them in a specific direction, which embodies the memory characteristic of memristors. As a consequence, parameters in the model vary continuously and cannot be determined by the states of neurons. Existing results on synchronization of memristive neural networks are useless to this model. To investigate the synchronization of the new model, the main difficulty is how to deal with the time-varying parameter mismatches between the drive and response networks. Since the error is unbounded and only utilizing output feedback control is not enough, a sliding mode controller is designed. An integral sliding surface is designed for the desired sliding motion, and a feasible control law is proposed. Moreover, an example is given to demonstrate the novelty of our model and to illustrate the effectiveness of the sliding mode controller.

本文提出了一种新型的忆阻神经网络模型。在新模型中，忆阻器的状态与忆阻器的初始电阻以及在特定方向上流过它们的电荷量有关，这体现了忆阻器的存储特性。结果，模型中的参数连续变化，无法由神经元状态确定。关于忆阻神经网络同步的现有结果对该模型没有用。为了研究新模型的同步性，主要困难是如何处理驱动器和响应网络之间的时变参数不匹配。由于误差是无限的，仅利用输出反馈控制是不够的，因此设计了滑模控制器。针对所需的滑动运动设计了整体滑动表面，并提出了可行的控制律。此外，给出了一个例子来说明我们模型的新颖性并说明滑模控制器的有效性。