基于状态区间逼近法的忆阻神经网络的稳定性分析与综合

The memristive neural networks are the important elements of neural networks. Compared with the traditional neural networks, memristive neural networks have many evident advantages in various fields such as secure communications, associative memory and pattern recognition, etc. Although the stability analysis and synthesis of memristive neural networks have provoked much attention, the related developments of their theories and applications do not reach the maturity stage yet, and there are still many problems to be solved. The project intends to investigate the stability analysis and synthesis of memristive neural networks by proposing a state interval approximation method which takes both the conservativeness and computational complexity into account. The main contents include: 1) the semi-global or local stability analysis of memristive neural networks will be investigated by setting up two reference systems. The relationship will be explored between the regions of admissible initial and convergence. 2) The synchronization and state estimation of memristive neural networks will be explored by building two response systems and two reduced-order estimators, respectively. The environment of networked communication will be considered among the systems, and the interval synchronization and interval estimation will be achieved, respectively. 3) The receding horizon control will be investigated based on the proposed state interval approximation method, and the research results will be verified through semi-physical simulation platform. The research of this project will be helpful to reveal the substantial behaviors and enrich the theory of memristor-based systems. It will also provide theoretical fundamentals and technical supports for the applications of memristive neural networks.

忆阻神经网络是一种重要的神经网络类型。与传统神经网络相比，忆阻神经网络在安全通信、联想记忆和模式识别等诸多方面都更具优势。尽管忆阻神经网络的稳定性分析与综合已经得到学者的密切关注，但其理论和应用研究都尚未成熟，仍有诸多问题亟待解决。在同时兼顾保守性和计算复杂性的前提下，本项目拟通过提出状态区间逼近法研究忆阻神经网络的稳定性分析与综合。研究内容主要包括：1)通过构造双参考系统，研究忆阻神经网络的半全局或局部稳定性问题，探究可行初值域与收敛域之间的关系；2)通过建立双响应系统和双降阶估计器研究忆阻神经网络的同步和状态估计问题，考虑系统之间的网络通讯环境，实现区间同步和区间估计；3)研究基于状态区间逼近法的滚动时域控制问题，结合半实物仿真平台，验证所得理论结果。项目研究将有助于揭示忆阻系统的本质特征，丰富忆阻系统的理论，为基于忆阻神经网络的应用提供必要的理论基础和技术支撑。

针对忆阻神经系统动力学分析与控制综合的若干挑战性问题，项目分别提出了基于指数逼近技术的事件触发控制策略、基于域分割的事件触发间歇式控制策略和离散时间的周期/动态周期事件触发策略，显著降低了控制所需的信号通信量，攻克了在低通信频率条件下实现系统高性能控制的难题，实现了低通信和计算资源下的同步控制。具体内容包括：1）借助利普希茨约束，将系统线性化，通过线性化系统的状态转移矩阵，构造指数逼近解，设定指数阈值，减小测量误差，变向达到了增加触发阈值，减少触发次数的目的，同时近似实现了点对点信号传输的控制性能；2）受“夹逼定理”原理启发，将非负时域划分为三个非负时域，通过Lyapunov泛函与各时域之间的隶属关系来确定是否对闭环系统施加控制，实现了事件触发控制的“按需控制”思想，改变了传统间歇式控制对工作和间歇时间的周期性和事先预设的限制；3）建立了离散时间周期/动态周期触发机制，扭转了周期触发机制难以在离散系统应用的局面，构造了基于采样周期的切换分段泛函，考虑了采样信号的锯齿特性，为周期采样技术在离散系统的分析与应用提供了完备方案。在周期触发的基础上，通过构造集员估计器，实现对系统未来一步状态的域估计。基于上述内容，项目共计发表SCI检索期刊论文15篇，其中IEEE汇刊10篇，发表EI检索及其他论文10篇，3篇入选ESI高被引论文。已培养硕士毕业生3名，正在培养的硕士研究生12名，博士研究生1名。