多种噪声诱导的随机切换神经网络的动态性及控制

Neural networks (NN) theory has been widely applied in various fields and achieved considerable success. In terms of theoretical researches and engineering applications, external noise and random switching are inevitable. However, existing works are concentrated on white noise and Markov switching stochastic neural networks, but for the research of colored noise and with state-dependent switching stochastic neural network is still in its infancy. This project will use Lyapunov stability theory, the generalized Itô formula, stochastic process, information entropy theory and so on to focus on the stability, robustness, input-to-state stability and controller design of Markov switching stochastic neural network, state-dependent switching stochastic neural network, colored noise induced state-dependent switching and colored noise induced Markov switching stochastic neural network. This project will give the precise interval partitioning of the changes of noise, delay and connecting weight matrices of neural networks with Markov switching and get the stability criteria for state-dependent switching and colored noise induced state-dependent switching stochastic neural network; establish the contacts between the complexity measurement indicator-information entropy to the stability, input to state stability for colored noise induced Markov switching stochastic neural network. This project will enrich the theory of stochastic switching system, reveal the mechanisms of dynamics behavior of various noises induced stochastic switching system and establish the theoretical foundation for the design and application of switched stochastic neural network in intelligent control of complex system.

神经网络理论广泛应用于多个领域并取得相当成功。从理论研究及工程应用而言，外部噪声及随机切换不可避免。已有的工作集中于白噪声及马氏切换领域，有色噪声及依赖于状态切换随机神经网络的研究尚处于起步阶段。本项目将利用李雅普诺夫稳定性理论、广义伊藤公式、随机过程、信息熵理论等方法研究马氏切换、依赖于状态切换、有色噪声诱导依赖于状态切换、有色噪声诱导马氏切换四种形式随机神经网络的稳定性、鲁棒性、输入状态稳定性及控制器设计。本项目将获得马氏切换神经网络的噪声、时延、联接权矩阵变化的大小的精确划分区间；得到白噪声和有色噪声诱导依赖于状态切换两种随机神经网络的稳定性准则；建立有色噪声诱导马氏切换随机神经网络复杂性度量指标信息熵与稳定性，输入状态稳定性之间联系。本项目将丰富随机切换系统理论，揭示多种噪声诱导随机切换系统动力学行为机理，为随机切换神经网络在复杂系统智能控制中的设计和应用奠定理论基础。

项目《多种噪声诱导的随机切换神经网络的动态性及控制》紧紧围绕依赖于状态切换的忆阻神经网络及马氏切换神经网络动态性及控制进行研究。在项目执行期间，课题组通力合作进行深入细致的研究。本项目从揭示内在固有规律、阐明外部控制原理、探究内外交互机制三个维度深入研究神经形态系统。重要科学发现包括：(1)揭示了状态依赖切换忆阻神经动力学系统内在的指数吸引集特性、收敛性和稳定性等固有规律，证明了复值忆阻神经网络与实值模型之间的相关等价性，系统地构建了基于微分包含理论的神经动力学系统分析和控制方法。利用非光滑分析工具，发展和完善了神经动力学系统分析和控制的微分包含理论。首次给出分数阶次在(0,2)区间内解的存在唯一性理论证明及有限时间稳定性充分条件；(2)阐明了外部控制对神经动力系统的作用原理，发展了面向右端不连续状态依赖切换神经网络的微分包含理论，设计一个依赖于初值及状态切换的闭环控制器，给出系统达到有限时间稳定和有界能量消耗的精确解析表达式；(3)探究了马氏切换神经动力学系统内在规律和外部刺激交互作用而产生的联想记忆机制，发展了神经网络的多吸引子与联想记忆相关理论与方法，其深入研究有利于神经元电路器件的集成和应用，为模拟大脑功能，用神经元电路器件实现信息动态存储与处理提供理论支撑。本项目共发表SCI论文20篇，获得省部级奖励2项，培养硕士研究生10余名，博士研究生3名，为10余名研究生提供部分资助。