智能参数变化系统的多吸引子理论及忆阻多值存储设计

Combining parameter models and neural networks, intelligent parameter-varying system will overcome the limitations of the traditional linear and nonlinear methods, and retain their advantages. This project is dedicated to study the multi-attractor theory and multi-valued storage design for intelligent parameter-varying system, then try to use memristive circuit simulation to verify the obtained theoretical results. Modern differential geometry theory and numerical method will be utilized to study the manifold parameter changes of topology in order to obtain the corresponding dynamical relationships between the multi-attractor and system parameters of the intelligent parameter-varying system. This project will study the control method for the multi-valued reading and writing on the basis of the dynamic response of the attractor. The efficiently fast dynamic information storage mechanism is established by memristor-based storage crossbars and dynamic responses of multi-attractors. At big data era, the traditional electronic memory speed, power consumption, and integration level are facing severe challenges. Meanwhile, the demand is arisen for computing power with high performance computing in practice. Intelligent parameter-varying system offers a new way to solve these technical bottlenecks via multi-attractor and multi-valued storage, which play an important role in theory and practice.

智能参数变化系统将参数模型和人工神经网络结合在一起，克服了传统线性和非线性方法的限制，又保留了各自的优点。本项目致力于研究智能参数变化系统的多吸引子理论与多值存储设计，并试图用忆阻电路仿真模拟来验证所获得的理论成果。本项目将利用现代微分流形几何理论和数值方法来研究参数变化的拓扑结构，获取智能参数变化系统的多吸引子与系统参数的动态对应关系、系统参数和吸引区域的动态映射关系。研究多值存储的读、写控制方法，通过系统多吸引子的动态响应来实现多值存储。结合忆阻的物理特点和忆阻存储阵列的特点，以及多吸引子的动态响应，建立基于忆阻的新型高效快速动态信息存储机制。大数据时代，传统电子存储器的速度、功耗及集成度等面临严峻挑战；同时，实际应用对计算能力的需求不断提升，超高性能计算正遇到存储墙、功耗墙等技术瓶颈。智能参数变化系统多吸引子和多值存储的研究给解决这些技术瓶颈提供了新的思路，具有重要的理论与应用价值。

忆阻具备的非易失性和多值性使其在设计神经网络电路中发挥了重要作用。本项目从忆阻神经网络出发，研究了智能参数变化系统的多吸引子理论及忆阻多值存储设计。利用右端不连续微分方程理论、不等式技巧和比较方法等研究了忆阻神经网络的Lagrange稳定性、指数镇定、全局镇定、有限时间镇定、固定时间镇定和无源性分析等动力学问题，获得了有关吸引区域与系统参数之间的关系，为构建智能参数变化系统的多吸引子理论与方法提供了有力支撑。提出了各类基于忆阻器的神经网络电路设计，设计中包含了忆阻神经网络电路的读写、擦除以及时序控制模块，探究了利用忆阻器建立新型高效快速动态信息存储的方法。依托本项目共培养9名博士生与16名硕士生，发表SCI源论文109篇，其中IEEE 汇刊论文62篇，包括 IEEE Transactions on Systems, Man, and Cybernetics: System论文14篇，IEEE Transactions on Cybernetics论文19篇，IEEE Transactions on Industrial Electronics论文2篇，IEEE Transactions on Neural Networks and Learning Systems论文12篇，IEEE Transactions on Fuzzy Systems论文5篇，IEEE Transactions on Automatic Control论文2篇。