基于T-S模糊模型的复杂非线性大系统的滤波器设计

【作者】 钟华；

【导师】 张洪斌；

【作者基本信息】 电子科技大学 ， 电路与系统， 2011， 硕士

【摘要】 随着现代科学技术的发展,许多现实生活中的系统比如:电力系统、核反应系统、航天系统、过程控制系统等等,系统的规模越来越大,结构也日趋复杂,同时还具备很强的非线性。解决这类系统问题的两大难点就是系统的大尺度特性和强非线性。大系统理论的提出,将一个高维数的系统从结构上视为多个子系统相互关联耦合而构成,从而可以将大系统的分析与设计建立在相对低维的子系统之上,降低了分析与设计的复杂度;同时针对系统的非线性问题,由于模糊建模的独特优越性,模糊系统理论已逐渐成为分析非线性系统的方法。作为控制的对偶问题,滤波问题对于信号估计、系统输出反馈控制方面有很大的工程指导意义。本文就通过利用大系统和模糊系统的理论相结合分析复杂非线性大系统的滤波器设计问题。论文的主要工作如下:本文的研究主要基于三类的模糊大系统:连续时间的模糊大系统、离散时间的模糊大系统、时延时变的模糊大系统。首先,针对一系列连续时间的模糊大系统,基于Lyapunov理论,同时采用分散的设计方法,分别分析了系统的H_∞, H 2,混合H_∞H₂滤波问题。将滤波器设计的充分条件转化为一系列的线性不等式。从而得到了连续系统的模糊滤波器设计。其次,针对离散时间的模糊大系统,同样采用分散的设计方法和Lyapunov理论,设计了系统的H_∞, H 2滤波器,同时采用带有线性矩阵不等式约束的凸优化方法设计混合H_∞H₂滤波器,在保证预定H_∞性能的同时使得H 2的性能指标最小。最后,针对时变时延的离散模糊大系统,基于赖于时延的分段二次Lyapunov泛函（DDPLKF）,采用自由权矩阵方法和分散的设计方法,分析了大系统的H_∞滤波器问题。最后通过一系列的线性矩阵不等式给出系统赖于时延的H_∞滤波器设计,以及不赖于时延的滤波器设计。更多还原

【Abstract】 Many real-life systems such as: power systems, nuclear reactor systems, space systems, process control systems, etc., have increasingly large in scale and complex in structure. And these systems are nonlinear systems. Two problems of such systems are the large-scale features and nonlinear. The methodologies of large-scale systems provide techniques through the manipulation of system structure in some way to overcome these problems. The large-scale systems are divided into numbers of subsystems which have connection between each other. Considering the nonlinear problems, due to the unique advantages of fuzzy modeling, fuzzy systems theory has gradually become the analysis method of nonlinear systems. As a dual problem of control, the filtering problem has an important significance for signal estimation, output feedback control system and so on. In this paper, by combining large-scale systems theory and fuzzy systems theory, we have studied the filter design problem of complex nonlinear large-scale system. The main work is as follows: our works are based on three kinds of systems: continuous time fuzzy large-scale system, discrete-time fuzzy large-scale system, and discrete-time fuzzy large-scale system with time-varying delay.1. We present the filter design for continuous time fuzzy large-scale system. Based on Lyapunov theory, we have analyze the H_∞, H₂, mixed H∞H₂filtering problem respectively with the decentralized approach. It will be shown that the resulting error system is asymptotically stable with guaranteed H_∞and generalized H₂ performance by solving a set of linear matrix inequalities.2. Based on Lyapunov theory and decentralized approach, we concerned with decentralized H_∞, H₂、H∞H₂filter design for discrete time fuzzy large-scale systems. The main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed H_∞performance. The sufficient conditions are established by solving a convex optimization problem with linear matrix inequalities constraint.3. We have studied the problem of delay-dependent H_∞filter design for a class of discrete-time nonlinear interconnected system with time-varying delays. Based on the delay-dependent piecewise Lyapunov-Krasovskii functional and with an improved free weighting matrix technique, the delay-dependent stability and a pre-scribed H_∞performance are guaranteed for overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible.更多还原