连续神经网络的状态估计问题研究

发布时间：2018-10-18 11:51

【摘要】：近年来,随着神经网络的快速发展,其在工程方面的应用也变得越来越多,但在实际的工程应用中,总会不可避免的出现诸如脆弱性、非线性、时滞等问题,此类问题的存在将直接导致只有部分神经元的状态信息可以通过网络输出。由此可见,尽可能准确的估计神经元的状态具有重要的科研价值以及实际意义。本文研究的内容是针对连续神经网络系统进行建模,并且基于Lyapunov稳定性定理,结合线性矩阵不等式(Linear Matrix Inequality,LMI)技术、矩阵分析技术等,讨论系统的稳定性并且对非脆弱性状态估计器设计方法进行验证。首先,针对具有时变时滞的连续神经网络系统,进行系统稳定性分析,并且讨论考虑加性增益变化的非脆弱性状态估计器研究方法。采用LMI方法,获得保证系统渐近稳定和满足其他约束条件的非脆弱性状态估计器存在的充分条件,以及状态估计器的增益,并对研究结果进行分析。其次,建立一类具有加性增益变化和时变时滞的连续神经网络模型,分析系统稳定性并设计非脆弱性状态估计器。定义连续神经网络增广系统和约束条件,选取李雅普诺夫函数并按照其稳定性定理,分析得到系统渐近稳定及状态估计器增益存在的充分条件。此时,非脆弱性状态估计器的设计实现就转化为求解相应LMI的可行解。再次,考虑到时变时滞的神经网络的稳定性和非脆弱性状态估计算法。采用乘性范数有界形式的估计器增益变化,利用Lipschitz条件刻画神经元状态依赖非线性扰动,研究带有非脆弱性的状态估计器。利用Lyapunov稳定性定理、矩阵分析技术、LMI技术、Leibniz-Newton公式,得到非脆弱性状态估计器存在的充分条件,以及标准LMI问题的可行解。最后,研究伴随噪声的连续神经网络系统稳定性和非脆弱性状态估计算法。利用两个不同的函数表示噪声,即系统产生的噪声序列和系统的观测噪声序列。结合上述神经网络模型,设计具有增益变量的非脆弱性状态估计器。通过分析误差动态增广系统的稳定性以及H?性能,得到非脆弱性状态估计器存在并且需要满足的LMI,即将非脆弱性状态估计器设计变换成用标准线性矩阵不等式方法解决凸优化问题,并通过实际算例说明研究的准确性。
[Abstract]:In recent years, with the rapid development of neural network, its application in engineering has become more and more, but in practical engineering applications, there are always inevitable problems such as vulnerability, nonlinearity, time-delay and so on. The existence of this kind of problem will directly result in the state information of some neurons can be outputted through the network. It can be seen that estimating the state of neurons as accurately as possible has important scientific research value and practical significance. The content of this paper is to model the continuous neural network system, and based on the Lyapunov stability theorem, combining with the linear matrix inequality (Linear Matrix Inequality,LMI) technology, matrix analysis technology, etc. The stability of the system is discussed and the design method of the non-fragile state estimator is verified. Firstly, the stability of continuous neural network systems with time-varying delays is analyzed, and the research method of non-vulnerability state estimators considering additive gain variation is discussed. By using the LMI method, the sufficient conditions for the existence of a non-fragile state estimator, which guarantees the asymptotic stability of the system and satisfies other constraints, are obtained, as well as the gain of the state estimator. The results of the study are analyzed. Secondly, a class of continuous neural network models with additive gain variation and time-varying delay are established to analyze the stability of the system and to design a non-fragile state estimator. The continuous neural network augmented system and its constraint conditions are defined. The Lyapunov function is selected and the sufficient conditions for the asymptotic stability of the system and the existence of the gain of the state estimator are obtained according to its stability theorem. In this case, the design and implementation of the non-vulnerability state estimator is transformed into a feasible solution to solve the corresponding LMI. Thirdly, the stability and non-vulnerability state estimation algorithms of neural networks with time-varying delays are considered. The gain variation of the estimator in the bounded form of multiplicative norm is used to characterize the neuron state dependent nonlinear disturbance by using the Lipschitz condition. The state estimator with non-vulnerability is studied. By using the Lyapunov stability theorem, matrix analysis technique, LMI technique and Leibniz-Newton formula, the sufficient conditions for the existence of non-fragile state estimators and the feasible solutions of the standard LMI problem are obtained. Finally, the stability and non-vulnerability state estimation algorithms for continuous neural networks with noise are studied. Two different functions are used to represent the noise, that is, the noise sequence generated by the system and the observed noise sequence of the system. Based on the above neural network model, a non-vulnerability state estimator with gain variables is designed. By analyzing the stability of dynamic augmentation system with error and H? The performance of the non-fragile state estimator is obtained and the LMI, that needs to be satisfied is transformed into a standard linear matrix inequality (LMI) method to solve the convex optimization problem. An example is given to illustrate the accuracy of the study.
【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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