【作者】 胡良剑；

【导师】 邵世煌； 吴让泉；

【作者基本信息】 东华大学 ， 控制理论与工程， 2004， 博士

【摘要】 随机性和模糊性是两种不同性质的不确定性，它们常常共存于系统中。由于他们涉及的数学工具不易结合，目前绝大多数系统分析和控制理论工作都只考虑用其中一种进行不确定性的建模，这样就造成一定的局限性。本文的目的是综合运用随机过程和模糊集合论的方法，通过更加精细地刻画系统不确定性，探索具有模糊随机不确定性的系统建模、分析和控制的新方法，并期望在最优性与鲁棒性之间寻求比较好的结合点。 当一个随机系统的输入或输出(观测)变量取值为模糊数，它就成为取值于模糊数空间上的随机系统，简称模糊随机系统。本文第一部分研究模糊随机系统的建模与分析的若干问题，推广了随机系统理论的一些结果。主要成果包括：提出了模糊随机变量协方差和反向协方差的概念；研究了二阶模糊随机变量的均方收敛性，并在此基础上得到了均方模糊随机分析、平稳模糊随机过程及其谱分解的若干定理；根据均方模糊随机分析理论，得到了输入为模糊随机过程的线性系统的输出输入统计特征关系方程；证明了Ito型模糊随机微分方程解的存在唯一性，并给出了Ito型线性模糊随机微分方程解的表达式，统计特征方程以及非线性模糊随机微分方程的数值解法；得到了模糊线性系统的稳定性和可观性条件、线性模糊随机系统统计特征方程和线性模糊随机系统的Kalman滤波算法；研究了当观测值是模糊数据时，线性回归模型的建立。 设控制对象是用Tag山一sugeno(T.s)模糊模型表示的非毕蜂琴攀{当模型参姆到统计特征已知的瞰嗓杆扰吟一就成为一个瞬娜咚模糊模型，本质上它是一个非线性随机微分系统。本文第二部分研彝雄舞具有随机参数扰动的模糊系统稳定性分析和控制碱，将T，s_瞬娜事钾控制理论的现有成果推广至随机T-s咖系终主要成果有二黄申了拿葬摧更多还原

【Abstract】 Randomness and fuzziness are two different kinds of uncertainty in complex systems. Since their mathematical tools are difficult to fuse, most of the known literature on system analysis and control considers only one of them to modeling the uncertainty, which results in some limitation. This dissertation is meant to combine the theory of stochastic processes and the theory of fuzzy sets to find some new methods of system modeling, analysis and control by describe uncertainty more minutely, and then to balance the optimization and the robustness.If the input or output (observation) variables of a stochastic system are fuzzy, the system becomes a stochastic system on fuzzy number space, and is called a fuzzy stochastic system. The results in the dissertation cover various aspects of fuzzy stochastic systems, including the following: The notions of covariance and cross-covariance are introduced. The mean-square (m.s.) convergences of the sequence of fuzzy random variables are discussed, and then some theorems on m.s. fuzzy stochastic analysis and stationary fuzzy stochastic processes are proved. The equations of the mean value functions and the covariance functions are established for dynamical systems whose inputs are fuzzy stochastic processes. An existence and uniqueness theorem of Ito fuzzy stochastic differential equations is proved, some explicit representations of solutions and the equations of statistical characteristics are deduced for linear fuzzy stochastic differential equations, and numericalmethods to nonlinear fuzzy stochastic differential equations are proposed, The conditions for stability and observability of fuzzy linear systems are derived. The Kalman filter algorithms of linear fuzzy stochastic systems are brought forward. Moreover, the statistical linear regression with fuzzy observation data is discussed.When the parameters of a Tagaki-Sugeno(T-S) fuzzy system are perturbed with random noise, the system turns to be a stochastic T-S system. Essentially, it is a nonlinear stochastic differential system. The second part ofthe dissertation focuses on the stability analysis and control of the stochastic T-S systems. The main contributions include: The conditions of global m.s.exponential stability, global almost surely (a,s.) exponential stability andglobal robust exponential stability are constructed. A set of linear matrix inequality (LMI) conditions is proposed to guarantee the clossd-loop m.s. (energy) stability and a.s. (path) stability. Performance-oriented controller synthesis is also discussed and muti-objective controller can be designed based on it. LMI design methods for robust controller ,H controller and robust H, controller of the stochastic T-S systems with unmodeling uncertainties are introduced. Finally, various controllers developed in this dissertation are applied to Lorenz chaos system with random perturbations, and compared with traditional controllers. All me analysis and controller designs are based on LMIs, that are facile to be solved by Matlab software更多还原