递归神经网络动力学行为若干问题研究

This project mainly study the robust stability, synchronization control and state estamition of neural networks with discontinuous activation functions. We will establish some Fuzzy neural networks with mode-dependent time delays, Markovian jumping parameters, Browian motion and discontinuous activation functions. These models may include stochastic disturbance terms, high-order terms, impulsive disturbances or reaction-diffusion terms. This project will solve several difficult problems of discontinuous neural networks in theoretical study and present some synchronization control methods with high function. Therefore this project will open up new way to studying neural networks with discontinuous activations. Our main original works are as follows: (1). To adopt the matrix inequality method to propose sufficient stability conditions for neural networks with mode-dependent time delays, Markovian jumping parameters, high-order terms and discontinuous activation functions; (2). To apply the matrix inequality method to present global stability criteria for Fuzzy neural networks with mode-dependent time delays, Markovian jumping parameters, stochastic disturbance terms, impulsive disturbance terms and discontinuous activation functions; (3). To utilize the matrix inequality method to bring out global stability conditions for Fuzzy neural networks with mode- dependent time delays, Markovian jumping parameters, stochastic disturbance terms, reaction-diffusion terms and discontinuous activation functions; (4). To use the matrix inequality method to derive global stability criteria for Fuzzy stochastic chaotic neural networks with mode-dependent time delays, Markovian jumping parameters, stochastic disturbance terms, discontinuous activation functions and impulsive disturbance terms or reaction-diffusion terms; to make use of the matrix inequality method to establish state-estamition conditions for Fuzzy stochastic neural networks with mode-dependent time delays, Markovian jumping parameters, stochastic disturbance terms, discontinuous activation functions and impulsive disturbance terms or reaction-diffusion terms. Our results will supply new intelligent algorithms for reactive power optimization of distribution network, promote deep theoretical development of related field.

本项目将研究不连续神经网络全局鲁棒稳定性、同步控制和状态估计问题。拟建立含模态依赖的各种时滞、具有马尔科夫参数切换和布朗运动的不连续高阶、模糊随机、随机脉冲和随机反应扩散神经网络模型，系统地解决不连续神经网络理论研究的一些难点问题，提出不连续神经网络的高性能同步控制方法，开辟不连续神经网络研究的新途径。主要创新性研究内容包括：1. 建立各种含模态依赖时滞的不连续马尔科夫切换高阶神经网络的全局稳定性矩阵不等式判据；2. 研究各种含模态依赖时滞的不连续马尔科夫切换模糊脉冲、模糊随机脉冲神经网络的稳定性问题；3. 建立各种含模态依赖时滞的不连续马尔科夫切换随机扩散、模糊随机扩散神经网络的全局稳定性矩阵不等式判据；4. 研究各种含模态依赖时滞的不连续马尔科夫切换脉冲、扩散等模糊随机混沌神经网络的同步控制和状态估计问题。上述成果将为配电网无功优化控制问题提供新的智能算法，推动相关领域理论的深入发展。

近年来递归神经网络广泛地应用于求解各种工程实际问题，诸如符号和图像处理，模式识别，联想记忆，并行计算以及优化和控制等。这些应用完全依赖于人们设计的神经网络的动力学行为。在本课题中，我们利用随机分析方法、LaSalle型不变原理、随机Halanay型不等式、拓扑度理论、Gu氏离散化L-K泛函方法、线性凸、二次凸组合方法、各种Jensen型积分不等式、基于Wirtinger的各种积分不等式、基于辅助函数的积分不等式、各种反凸组合不等式、高阶反凸组合不等式、Yang-Yang不等式、Liu-Zhang不等式、Finsler引理、Briat引理、Gu氏消变量引理以及Zeng氏自由权矩阵不等式等技术，研究了具模态依赖混合时滞的随机Markov跳跃C-GNN时滞依赖指数稳定化，具混合时滞、非光滑行为函数和反Lipschitz神经激励函数的C-GNN平衡点存在、唯一和全局指数稳定性，具模态依赖时变时滞的Markov跳跃C-GNN全局一致指数鲁棒随机收敛性，具混合时滞和Markov切换的中立型NN全局一致鲁棒指数随机收敛性和稳定性，具混合时滞的随机Markov混沌NN的指数同步和时滞依赖全局鲁棒同步，含模态依赖混合时滞的中立型随机MarkovNN的鲁棒自适应同步，具漏泄时滞的随机Markov反应扩散NN均方意义下全局渐近稳定性，具离散和连续分布时滞的随机Markov混沌NN的全局鲁棒反同步，基于忆阻的含时变时滞混沌NN的时滞依赖全局渐近同步，具漏泄时滞和脉冲扰动的随机模糊MarkovNN、具混合时滞和漏泄时滞的模糊脉冲细胞NN、具离散和无穷分布时滞的模糊Markov细胞NN、具脉冲扰动和时变混合时滞的随机模糊MarkovNN的全局渐近稳定性，具时变离散和分布时滞中立型参数不确定NN的无源性，具漏泄和混合时滞的中立型脉冲NN、含时变离散和连续分布时滞的中立型切换HopfieldNN的全局渐近稳定性，线性耦合神经网络全局渐近同步稳定性。