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基于T-S模糊模型的非线性离散系统的H_∞滤波

H∞ Filtering for Nonlinear Discrete-time Systems Based on T-S Fuzzy Model

作者: 专业:应用数学 导师:张小美 年度:2010 学位:硕士  院校: 南通大学

Keywords

T-S fuzzy model, discrete systems, H_∞filtering, delay, sensor faults

        非线性系统的稳定性分析和设计是控制理论领域的一个重要的研究课题.Takagi-Sugeno(T-S)模糊方法是研究非线性系统的一种有效方法,原因是它可以运用Lyapunov稳定性理论来进行系统分析和设计.非线性系统的滤波问题由于在信号合成,通讯和控制中的实际应用使其成为一个研究热点.通常Kalman滤波应用比较广泛,然而在系统模型和噪声统计特性存在不确定性的条件下Kalman滤波的应用受到限制, H_∞滤波可以有效地解决Kalman滤波所遇到的问题,不仅估计精度高,而且具有鲁棒性.本文主要基于T-S模糊模型,对离散时间非线性系统的H_∞滤波进行研究,主要做了以下几个工作:(1)研究了在系统的测量出现时滞情况下离散系统的模糊H_∞滤波问题.利用模糊Lyapunov函数方法,线性矩阵不等式方法等,研究了滤波误差系统的时滞依赖稳定性条件.在此基础上,给出了H_∞滤波器的设计方案.并举例证明了上述方法的有效性.(2)研究了在系统的测量出现数据丢失情况下离散时滞模糊系统的H_∞滤波问题.假设测量数据丢失现象服从Bernoulli随机二点分布.首先,利用基依赖的Lyapunov泛函方法对滤波误差系统的H_∞性能进行分析,然后,利用线性矩阵不等式技巧设计H_∞滤波器.最后通过例子说明所给方法的有效性.(3)研究了存在随机传感器故障时离散时滞模糊系统的H_∞滤波问题.假设传感器故障能够用服从具体分布律的随机变量来刻画.目的是设计H_∞滤波器使得滤波误差系统在均方意义下渐近稳定并且具有指定的H_∞抑制水平.理想的滤波器借助一组线性矩阵不等式的可行解得到.
    The problem of stability analysis and design for nonlinear systems is an important subject of control theory. Takagi-Sugeno (T-S) fuzzy approach is an effective method of studying nonlinear systems, because it can fully use Lyapunov stability theory to deal with stability analysis and design for nonlinear systems. The problem of filtering for nonlinear systems becomes a very important subject because it is widely applied in many fields such as compositing signal, communication, controlling system. In general conditions, Kalman filtering technique has been applied extensively. When there are uncertainties in dynamic model and the statistics of noise sources are not fully known, the application of Kalman filtering is restricted. H_∞filtering can solve the problem encountered in the applications of Kalman filtering with high accuracy and robustness. Based on the T-S model , this paper deals with H_∞filtering for discrete-time systems. The main contents in this thesis are as follows:(1) Fuzzy H_∞filtering for discrete-time systems with delayed measurement is investigated. By utilizing Lyapunov stability theory and linear matrix inequality method, delay-dependent sufficient conditions which guarantee the stability of the filtering error systems are established. Then, the design approach of such a filter is presented. A numerical example is given to demonstrate the effectiveness of the proposed method.(2) H_∞filtering for discrete time-delay fuzzy systems with missing measurement is discussed. The phenomenon of the missing measurement is assumed to satisfy the Bernoulli random binary distribution and the time-delay is time-invariant. H_∞performance of the filter error system is firstly analyzed by using a basis-dependent Lyapunov functional approach. Then, linear matrix inequality techniques are utilized to design theH_∞filter. An illustrative example is provided to show the effectiveness of the proposed approach.(3) H_∞filtering for discrete time-delay fuzzy systems with probabilistic sensor faults is studied. It is assumed that the probabilistic sensor reductions can be modeled by using a random variable that obeys a specific distribution law. The aim is to design a robustH_∞filter such that the filtering error system is asymptotically mean-square stable with prescribedH_∞noise attenuation level. The design filter is obtained based on the feasible solutions of a set of linear matrix inequalities.
        

基于T-S模糊模型的非线性离散系统的H_∞滤波

摘要6-7
Abstract7-8
符号说明9-10
第一章 绪论10-16
    1.1 课题的提出及意义10-11
    1.2 H_∞滤波问题的研究背景11-12
    1.3 T-S模糊系统描述12-14
    1.4 H∞滤波问题的研究现状14-16
第二章 预备知识16-22
    2.1 常微分方程的稳定性及判定定理16-17
        2.1.1 常微分方程稳定性概念16
        2.1.2 Lyapunov稳定性定理16-17
    2.2 差分方程稳定性判定定理17-18
    2.3 H_∞范数18-20
    2.4 线性矩阵不等式方法(LMI)20-22
        2.4.1 LMI的一般表示20
        2.4.2 标准LMI问题20-22
第三章 测量出现时滞时非线性离散系统的模糊H∞滤波22-32
    3.1 引言22
    3.2 问题描述22-25
    3.3 H∞滤波器设计25-29
    3.4 仿真例子29-31
    3.5 小结31-32
第四章 部分测量数据丢失时离散时滞模糊系统的H∞滤波32-43
    4.1 引言32
    4.2 问题描述32-35
    4.3 性能分析35-38
    4.4 滤波器设计38-41
    4.5 仿真例子41-42
    4.6 小结42-43
第五章 存在随机传感器故障的离散时滞模糊系统的H_∞滤波43-59
    5.1 引言43
    5.2 问题描述43-45
    5.3 性能分析45-53
    5.4 滤波器设计53-58
    5.5 小结58-59
参考文献59-64
致谢64-65
作者攻硕期间发表的论文及参加的项目65
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