具有混合多时滞的忆阻神经网络稳定性分析与有限时间控制

The stability analysis and control of memristive neural networks are the hot topics in the field of brain-like computation. Distributed and discrete multiple delays (mixed multiple delays) are the essential characteristics of memristive neural networks in practical application. By deeply analyzing the memristive neural networks with mixed multiple delays, considering the memristor switching as well as the hybrid multiple delays, this project investigates the stability and finite-time control. The main contents are as follows. Designing the circuit of memristive neural networks with mixed multiple delays and building the mathematical model. Due to the discontinuous problem of the system caused by the switching feature of memristor, we propose the theory of differential inclusions as well as the nonsmooth analysis method to analyze the system stability, and to accomplish the stabilization by designing proper feedback controls. Further we adopt the scheme combined with delayed control and adaptive control to compensate the effects of mixed multiple delays and then to discuss the finite-time stabilizability. Meanwhile, the finite-time robust control of system under disturbance is realized. The results of this project will provide new research approaches for analysis and control of memristive neural networks and theoretical foundation for the designing, exploitation and establishment of nonlinear systems with mixed multiple delays.

忆阻神经网络的稳定性分析与控制是类脑计算领域的热点问题。分布时滞和离散多时滞（混合多时滞）是目前实际应用中忆阻神经网络的本质特征。本项目对具有混合多时滞的忆阻神经网络进行深入分析，综合考虑其忆阻切换、多时滞混杂等固有属性，研究系统的稳定性与有限时间控制。主要研究内容包括：设计具有混合多时滞的忆阻神经网络电路并建立系统模型；针对忆阻状态切换特性导致系统不连续的问题，采用微分包含理论和非光滑分析方法分析系统的稳定性，并设计反馈控制实现系统的镇定；采用延迟控制和自适应控制相结合的方案补偿混合多时滞给系统带来的影响，分析系统的有限时间可镇定性，同时实现扰动影响下系统的有限时间鲁棒控制。本项目的成果，一方面为忆阻神经网络的分析与控制提供新的研究思路；另一方面为具有混合多时滞的非线性系统的设计、开发与构建提供理论依据。

本项目围绕忆阻神经网络模拟人脑工作机制的应用需求，分析其分布时滞、离散多时滞和随机扰动等典型特征，构建从实际电路角度能够反映人脑学习机制的具有混合多时滞的忆阻神经网络电路系统，研究了其稳定性、可镇定性和有限时间控制等动力学行为，发展形成了具有混合多时滞的忆阻神经网络系统动力学分析与控制的一般性理论框架，为忆阻神经网络动力学分析与控制提供新思路、新技术与新方法。. 根据项目研究计划，项目组成员经过三年努力，系统地开展了各项相关研究工作，圆满地完成了预期研究目标。目前，在本项目（61703377）资助下，总计发表或录用控制与人工智能领域学术论文20篇，其中SCI收录源期刊论文15篇，IEEE汇刊5篇，会议论文5篇，入选ESI高被引论文1篇，授权国家发明专利3项，获批软件著作权5项。此外，培养硕士研究生10名，其中毕业1名，在读9名。