时滞神经网络系统的非脆弱状态估计
发布时间：2018-11-20 15:50
【摘要】：近年来,递归神经网络(RNNs)系统被广泛的应用到模式识别、图像处理、联想记忆过程、最优化问题等各个方面。本文研究时滞神经网络的稳定性分析和状态估计问题,但在实际系统中,却不可避免地出现时滞、非线性、不确定性等现象。在这样一个拥有大量神经元并且神经元之间高度互联的神经网络模型中,要完全获知所有神经元的状态信息往往是非常困难的,这就要求人们近似地估计出这些神经元的状态。基于这些考虑,对时滞递归神经网络的状态估计理论的研究就具有非常重要的理论价值和实际意义。本文针对神经网络系统研究系统的稳定性和非脆弱状态估计问题,并给出更加宽松的稳定性条件,得到保守性更弱的结果。其主要结果包括四个方面:第一部分:针对具有常时滞的离散神经网络系统,设计非脆弱状态估计器。基于Lyapunov-Krsasovskii稳定性理论和一些矩阵不等式的变换技巧,以线性矩阵不等式(LMI)的形式给出神经网络系统时滞渐近稳定的充分条件,并求得状态估计器的增益。第二部分:研究系统模型和估计器模型同时存在不确定性因素的神经网络状态估计问题。通过构造合适的李雅普诺夫函数,得到系统渐近稳定及状态估计器增益存在的充分条件。在这个条件下,非脆弱状态估计器的设计实现就转化为求解一个相应的线性矩阵不等式的可行解。第三部分:考虑到时间驱动机制的网络冗余现象,在时滞离散神经网络系统中引入事件驱动机制,实现有效地解决这一问题。通过构造新的Lyapunov泛函,获得保证系统在均方意义下渐近稳定的时滞相关充分条件,以LMI的形式给出时滞相关的神经网络状态估计器的设计方法,并得到标准线性矩阵不等式问题的可行解。第四部分:研究依概率分布的时变时滞神经网络系统非脆弱状态估计问题。使用相互独立的伯努利随机过程和布朗运动分别刻画依概率分布的时变时滞与随机发生非线性扰动现象。通过设计一个非脆弱状态估计器,获得保证系统稳定的时滞相关充分条件,通过求解一个相应的线性矩阵不等式得到估计器的增益矩阵。
[Abstract]:In recent years, recursive neural network (RNNs) systems have been widely used in pattern recognition, image processing, associative memory processes, optimization problems and so on. In this paper, the stability analysis and state estimation of neural networks with time-delay are studied. However, in practical systems, delay, nonlinearity, uncertainty and so on are inevitable. In such a neural network model with a large number of neurons and highly interconnected neurons, it is often very difficult to obtain the state information of all neurons completely, which requires people to estimate the state of these neurons approximately. Based on these considerations, it is of great theoretical and practical significance to study the state estimation theory of recurrent neural networks with time delay. In this paper, the stability and non-fragile state estimation of neural network systems are studied, and the more relaxed stability conditions are given, and the less conservative results are obtained. The main results include four aspects: in the first part, a non-fragile state estimator is designed for discrete-time neural networks with constant delays. Based on Lyapunov-Krsasovskii stability theory and some transformation techniques of matrix inequalities, a sufficient condition for the asymptotic stability of neural network systems with time delay is given in the form of linear matrix inequalities (LMI), and the gain of the state estimator is obtained. In the second part, the problem of neural network state estimation with uncertainties in both the system model and the estimator model is studied. By constructing a suitable Lyapunov function, sufficient conditions for the asymptotic stability of the system and the existence of the gain of the state estimator are obtained. Under this condition, the design and implementation of a non-fragile state estimator is transformed into a feasible solution for solving a corresponding linear matrix inequality (LMI). In the third part, considering the network redundancy of time-driven mechanism, the event-driven mechanism is introduced into the time-delay discrete neural network system to solve this problem effectively. By constructing a new Lyapunov functional, the delay-dependent sufficient conditions for the asymptotic stability of the system in the mean square sense are obtained, and the design method of the delay-dependent neural network state estimator is given in the form of LMI. The feasible solution of the standard linear matrix inequality problem is obtained. In the fourth part, the non-fragile state estimation problem of time-varying time-delay neural network systems with probability distribution is studied. Independent Bernoulli stochastic processes and Brownian motions are used to characterize the time-varying delays and random nonlinear perturbations respectively. By designing a non-fragile state estimator, the delay-dependent sufficient conditions for the stability of the system are obtained, and the gain matrix of the estimator is obtained by solving a corresponding linear matrix inequality.
【学位授予单位】：东北石油大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183
本文编号：2345318
[Abstract]:In recent years, recursive neural network (RNNs) systems have been widely used in pattern recognition, image processing, associative memory processes, optimization problems and so on. In this paper, the stability analysis and state estimation of neural networks with time-delay are studied. However, in practical systems, delay, nonlinearity, uncertainty and so on are inevitable. In such a neural network model with a large number of neurons and highly interconnected neurons, it is often very difficult to obtain the state information of all neurons completely, which requires people to estimate the state of these neurons approximately. Based on these considerations, it is of great theoretical and practical significance to study the state estimation theory of recurrent neural networks with time delay. In this paper, the stability and non-fragile state estimation of neural network systems are studied, and the more relaxed stability conditions are given, and the less conservative results are obtained. The main results include four aspects: in the first part, a non-fragile state estimator is designed for discrete-time neural networks with constant delays. Based on Lyapunov-Krsasovskii stability theory and some transformation techniques of matrix inequalities, a sufficient condition for the asymptotic stability of neural network systems with time delay is given in the form of linear matrix inequalities (LMI), and the gain of the state estimator is obtained. In the second part, the problem of neural network state estimation with uncertainties in both the system model and the estimator model is studied. By constructing a suitable Lyapunov function, sufficient conditions for the asymptotic stability of the system and the existence of the gain of the state estimator are obtained. Under this condition, the design and implementation of a non-fragile state estimator is transformed into a feasible solution for solving a corresponding linear matrix inequality (LMI). In the third part, considering the network redundancy of time-driven mechanism, the event-driven mechanism is introduced into the time-delay discrete neural network system to solve this problem effectively. By constructing a new Lyapunov functional, the delay-dependent sufficient conditions for the asymptotic stability of the system in the mean square sense are obtained, and the design method of the delay-dependent neural network state estimator is given in the form of LMI. The feasible solution of the standard linear matrix inequality problem is obtained. In the fourth part, the non-fragile state estimation problem of time-varying time-delay neural network systems with probability distribution is studied. Independent Bernoulli stochastic processes and Brownian motions are used to characterize the time-varying delays and random nonlinear perturbations respectively. By designing a non-fragile state estimator, the delay-dependent sufficient conditions for the stability of the system are obtained, and the gain matrix of the estimator is obtained by solving a corresponding linear matrix inequality.
【学位授予单位】：东北石油大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183
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