马尔可夫跳跃神经网络与基于忆阻器Chua的电路的稳定性

发布时间：2018-09-07 10:57

【摘要】：由于神经网络经常出现稳定周期混沌现象,因此被广泛的应用于图像处理、模式识别、联想记忆、组合优化等众多领域中。在本文中,基于微分包含、非光滑分析、Lyapunov稳定性理论及线性矩阵不等式技术,通过设计合适的控制器,系统的研究了具有混合时变延时和间断激励函数的马尔可夫跳跃神经网络的指数状态估计和基于忆阻器Chua的自适应反馈震荡电路的混沌反同步控制问题。主要内容如下:(1)研究了具有混合时变延时和间断激励函数的马尔可夫跳跃神经网络的指数状态估计。其中测量方程的非线性扰动符合局部Lipschitzian条件,通过在李雅普诺夫函数中引入三重积分项和四重积分项,使在不同的系统模型中李雅普诺夫矩阵也是不同的。应用非光滑分析理论和随机分析技术,设计全阶的状态估计使相应的误差系统均方指数稳定。通过求解一组线性矩阵不等式可以实现模型依赖和时滞相关估计。(2)研究了基于忆阻器Chua的自适应反馈震荡电路的混沌反同步控制问题。首先根据忆阻器本身的电流-电压特性,将其误差系统分为四种不同的情况分别予以讨论。其次利用Lyapunov-Krasovskii泛函稳定性理论和方法,设计了能使响应系统与相应的驱动系统反同步的自适应状态反馈控制器。
[Abstract]:Neural networks are widely used in image processing, pattern recognition, associative memory, combinatorial optimization and many other fields because of the phenomenon of stable periodic chaos. In this paper, based on the Lyapunov stability theory of differential inclusions, nonsmooth analysis and linear matrix inequality (LMI) techniques, appropriate controllers are designed. The exponential state estimation of Markov hopping neural networks with mixed time-varying delay and discontinuous excitation function and chaotic anti-synchronization control of adaptive feedback oscillating circuits based on Chua are studied systematically. The main contents are as follows: (1) the exponential state estimation of Markov hopping neural networks with mixed time-varying delay and discontinuous excitation function is studied. The nonlinear perturbation of the measurement equation conforms to the local Lipschitzian condition. By introducing the triple integral term and the fourth integral term into the Lyapunov function, the Lyapunov matrix is different in different system models. Based on the theory of non-smooth analysis and stochastic analysis, a full-order state estimation is designed to stabilize the mean square exponent of the corresponding error system. Model dependence and delay-dependent estimation can be realized by solving a set of linear matrix inequalities (LMIs). (2) chaotic anti-synchronization control of adaptive feedback oscillating circuits based on Chua is studied. Firstly, according to the current-voltage characteristics of the resistor itself, the error system is divided into four different cases. Secondly, using the Lyapunov-Krasovskii functional stability theory and method, an adaptive state feedback controller is designed, which can synchronize the response system with the corresponding drive system.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP183;O231

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