一种新的复杂系统模糊辨识方法

针对一阶Takagi-Sugeno模型辨识复杂系统的困难,提出一种新的模糊模型.这种模 型的结构在一阶Takagi-Sugeno模型的基础上,再进行一次非线性映射.文中运用卡尔曼滤 波算法的模糊神经元网络实现了这种模型.仿真结果表明该方法辨识精度高,且有良好的 实用性.     

模糊聚类与最小二乘相结合建立非线性系统模型

提出一种模糊聚类与最小二乘相结合的辨识方法.该方法利用基于模糊似然函数的模糊聚类算法确定系统的模糊划分数目,进而对应聚类个数建立相应的Takagi-Sugeno局部线性化模型,并结合递推最小二乘法,完成系统的辨识.该方法可使模糊模型的结构辨识和参数辨识同时完成,从而实现模糊模型的在线辨识.该方法辨识速度快,精确度高.仿真结果验证了该方法的有效性.     

基于多分辨率分析的T-S模糊系统

目前模糊系统缺乏保持辨识精度与模糊语义最佳折中的有效辨识方法,其主要原因在于缺乏系统的优化结构辨识方法.因此,本文从时-频域角度构造出基于多分辨率分析的T-S(Takagi-Sugeno)模糊系统拓扑结构.然后,采用具有多分辨率特点的B-样条尺度函构造模糊隶属函数,根据投影算法和模糊隶属函数相异测度给出了模糊系统结构辨识算法.仿真结果验证了这种模糊系统及其结构辨识算法的有效性.     

基于拟非线性模糊模型的复杂系统模糊辨识

针对一阶Takagi-Sugeno（以下简称T-S）模型辨识复杂系统的困难，本文提出了一种新的拟非线性模糊模型。即在一阶T-S模型的基础上，再进行一次非线性映射。这种模糊模型不仅具有较高的辨识精度，而且具有良好的泛化功能。运用改进的FCM（Fuzzy-C-Means）模糊聚类方法，辨识该模糊模型的结构，与以往的方法比较，极大地简化了结构辨识的复杂性。仿真结果进一步说明了该方法的有效性。     

一类非线性离散时间系统的模糊辨识

对一类非线性离散时间系统提出了模糊辨识方法,此方法用与未知参数向量成线性关系的模糊逻辑系统作为辨识模型,并通过自适应学习律对此模糊逻辑系统中的未知参数进行自适应调节,文中证明了此方法可使辨识误差收敛到原点的一个邻域内。仿真结果验证了此方法的有效性。     

广义模糊神经网络

从非线性系统本身的物理背景出发,根据系统本身的内在特性、先验知识和经验建立系 统辨识模型,提出了广义模糊神经网络(GFNN).文中证明了GFNN的函数逼近定理,并据此提 出了GFNN的结构自组织和参数自学习算法.GFNN在预设的辨识精度下能自动辨识系统的网 络结构以及进行参数自学习,实现GFNN网络结构的真正在线自组织.仿真结果表明,对于慢时 变非线性对象,GFNN表现出了很强的非线性逼近能力,是模糊逻辑系统与人工神经网络两类方 法的比较成功的融合.     

基于模糊对向神经网络的非线性动态系统辨识器

模糊对向神经网络（ＦＣＰ）在功能上同模糊逻辑系统的ＴＳ模型是等价的,它具有神经网络和模糊逻辑系统各自的优点,因而适宜作辨识模型。     

基于T-S模糊逻辑推理的非线性预测模型

建立了基于Takagi-Sugeno模糊逻辑推理的局部多元回归模糊模型(LMRF模型)，将其用于具有小样本数据和非线性特点的宏观非线性系统预测。在多维空间下用C-聚类方法划分模糊子空间，采用带3参数的广义高斯隶属函数．提高了预测的精度，后件参数的辨识采用最小二乘法将减少计算复杂度，交通流量预测实例表明，基于T-S模糊推理的局部多元回归模型用于交通系统能准确地表达交通流量与社会经济的复杂关系，相对于多元线性回归预测模型精度要高得多。     

基于参数辨识和T-S模糊模型的一类非线性系统镇定控制器设计

针对一类非线性不确定控制系统,首先采用参数辨识的方法构造出对应的Takagi-Sugeno（T-S）模糊模型;然后运用平行分布补偿（PDC）控制器设计方法进行系统的稳定控制器设计;最终达到镇定原非线性系统的目的.给出一种从T-S模糊模型参数辨识到PDC控制器设计的非线性控制器的设计方法.针对单级倒立摆系统的仿真结果验证了所提出方法的有效性.     

基于广义模糊基函数的多变量模糊模型及其辨识方法

利用模糊穴位映射理论，提出一种有效描述复杂多变量系统的模糊模型－－广义模糊基函数展开式，它可方便地处理多输入多输出系统的语言和系统信息，并可逼近任意非线性函数，是一种通用的多变量模糊逻辑系统模型。利用语言信息，提出一种新的自适应参数辨识方法－－改进的Ｗｉｄｒｏｗ－Ｈｏｆｆ学习规则，仿真结果验证了它的有效性。     

MULTIVARIABLE FUZZY GENERALIZED PREDICTIVE CONTROL

A Takagi-Sugeno (T-S) fuzzy model is used to express non-linear dynamic systems with time-delay in this paper, and an on-line identification algorithm is presented regarding its parameters and structures. A multivariable fuzzy generalized predictive control approach is proposed based on the identified fuzzy model by means of the generalized predictive control principle. The closed-loop stability is analyzed in detail. A simulation study for the multivariable load system of a boiler-turbine unit shows that the approach is superior to convention load control systems.     

Model construction, rule reduction, and robust compensation forgeneralized form of Takagi-Sugeno fuzzy systems

This paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction, rule reduction, and robust compensation for nonlinear systems. The model construction part replaces the nonlinear dynamics of a system with a generalized form of Takagi-Sugeno fuzzy systems, which is newly developed by us. The generalized form has a decomposed structure for each element of A_i and B_i matrices in consequent parts. The key feature of this structure is that it is suitable for constructing IF-THEN rules and reducing the number of IF-THEN rules. The rule reduction part provides a successive procedure to reduce the number of IF-THEN rules. Furthermore, we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models. The robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties. Finally, two examples demonstrate the utility of the systematic procedure developed     

Extending the functional equivalence of radial basis functionnetworks and fuzzy inference systems

We establish the functional equivalence of a generalized class of Gaussian radial basis function (RBFs) networks and the full Takagi-Sugeno model (1983) of fuzzy inference. This generalizes an existing result which applies to the standard Gaussian RBF network and a restricted form of the Takagi-Sugeno fuzzy system. The more general framework allows the removal of some of the restrictive conditions of the previous result.     

基于拟非线性模糊模型的复杂系统模糊辨识

针对一阶Takagi－Sugeno[以下简称T－S]到模型辨识复杂系统的困难，本文提出了一种新的拟非线性模糊模型．即在一阶T－S模型的基础上，再进行一次非线性映射．这种模糊模型不仅具有较高的辨识精度，而且具有良好的泛化功能．运用改进的FCM（FuzzyC－Means）模糊聚类方法，辨识该模糊模型的结构，与以往的方法比较，极大地简化了结构辨识的复杂性．仿真结果进一步说明了该方法的有效性．     

Observers for Takagi-Sugeno fuzzy systems

We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.     

T-S model based indirect adaptive fuzzy control using online parameter estimation

A parameter estimation scheme with an appropriate adaptive law for updating the parameters is designed and analyzed based on the Lyapunov theory for the general MIMO Takagi-Sugeno (T-S) fuzzy models. The parameters of the Takagi-Sugeno fuzzy models can be estimated by observing the behavior of the system and with the online parameter estimator, any type of fuzzy controllers works adaptively to the parameter perturbation. In order to show the applicability of the proposed estimator, an existing fuzzy state feedback controller is adopted and indirect adaptive fuzzy control design with the proposed estimator is shown. From the numerical simulations and experiments, it is shown that the derived adaptive law works for the estimation model to follows the parameterized plant model and the overall control system has robustness to the parameter perturbation.     

A new T-S fuzzy model predictive control for nonlinear processes

In this paper, a novel fuzzy Generalized Predictive Control (GPC) is proposed for discrete-time nonlinear systems via Takagi-Sugeno system based Kernel Ridge Regression (TS-KRR). The TS-KRR strategy approximates the unknown nonlinear systems by learning the Takagi-Sugeno (TS) fuzzy parameters from the input-output data. Two main steps are required to construct the TS-KRR: the first step is to use a clustering algorithm such as the clustering based Particle Swarm Optimization (PSO) algorithm that separates the input data into clusters and obtains the antecedent TS fuzzy model parameters. In the second step, the consequent TS fuzzy parameters are obtained using a Kernel ridge regression algorithm. Furthermore, the TS based predictive control is created by integrating the TS-KRR into the Generalized Predictive Controller. Next, an adaptive, online, version of TS-KRR is proposed and integrated with the GPC controller resulting an efficient adaptive fuzzy generalized predictive control methodology that can deal with most of the industrial plants and has the ability to deal with disturbances and variations of the model parameters. In the adaptive TS-KRR algorithm, the antecedent parameters are initialized with a simple K-means algorithm and updated using a simple gradient algorithm. Then, the consequent parameters are obtained using the sliding-window Kernel Recursive Least squares (KRLS) algorithm. Finally, two nonlinear systems: A surge tank and Continuous Stirred Tank Reactor (CSTR) systems were used to investigate the performance of the new adaptive TS-KRR GPC controller. Furthermore, the results obtained by the adaptive TS-KRR GPC controller were compared with two other controllers. The numerical results demonstrate the reliability of the proposed adaptive TS-KRR GPC method for discrete-time nonlinear systems.     

Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators

The fuzzy rough set model and interval-valued fuzzy rough set model have been introduced to handle databases with real values and interval values, respectively. Variable precision rough set was advanced by Ziarko to overcome the shortcomings of misclassification and/or perturbation in Pawlak rough sets. By combining fuzzy rough set and variable precision rough set, a variety of fuzzy variable precision rough sets were studied, which cannot only handle numerical data, but are also less sensitive to misclassification. However, fuzzy variable precision rough sets cannot effectively handle interval-valued data-sets. Research into interval-valued fuzzy rough sets for interval-valued fuzzy data-sets has commenced; however, variable precision problems have not been considered in interval-valued fuzzy rough sets and generalized interval-valued fuzzy rough sets based on fuzzy logical operators nor have interval-valued fuzzy sets been considered in variable precision rough sets and fuzzy variable precision rough sets. These current models are incapable of wide application, especially on misclassification and/or perturbation and on interval-valued fuzzy data-sets. In this paper, these models are generalized to a more integrative approach that not only considers interval-valued fuzzy sets, but also variable precision. First, we review generalized interval-valued fuzzy rough sets based on two fuzzy logical operators: interval-valued fuzzy triangular norms and interval-valued fuzzy residual implicators. Second, we propose generalized interval-valued fuzzy variable precision rough sets based on the above two fuzzy logical operators. Finally, we confirm that some existing models, including rough sets, fuzzy variable precision rough sets, interval-valued fuzzy rough sets, generalized fuzzy rough sets and generalized interval-valued fuzzy variable precision rough sets based on fuzzy logical operators, are special cases of the proposed models.     

On the Stability of Takagi–Sugeno Fuzzy Systems With Time-Varying Uncertainties

This paper studies the problems of stability analysis of Takagi-Sugeno free fuzzy systems with time-varying uncertainties. In our prior study, we represented the time-varying uncertainty incurred in characteristic interval matrices in terms of the stability of Takagi-Sugeno free fuzzy systems with consequent parameter uncertainties. Based on Mayer's convergent theorem for powers of single interval matrix and its generalization, we further proposed some sufficient conditions for the Takagi-Sugeno free fuzzy system with time-varying uncertainties to be globally asymptotically stable. In this paper, we propose the notion of simultaneously nilpotent interval matrices to investigate the Takagi-Sugeno free fuzzy system with time-varying uncertainties to be strongly stable within steps, where relates to the dimension of interval matrices. Moreover, a unique situation for the deterministic Takagi-Sugeno free fuzzy system to be strongly stable within steps is derived as well, where relates to the dimension of characteristic matrices for the deterministic Takagi-Sugeno free fuzzy system.     

软腔体柔性机械臂的T-S模糊建模方法的研究

提出一种利用T-S模糊模型的柔性机械臂建模方法;柔性机械臂是一个高度复杂、高度非线性、高度耦合的非线性时变系统,而模糊模型本质上是一种非线性模型,可以任意精度逼近任何非线性系统;利用减法聚类算法离线辨识了T-S模型的前件参数,同时利用最小二乘法求得了T-S模型的后件参数;最后将模型的仿真结果和实验结果进行了对比分析,验证了模型的准确性;由此表明,柔性机械臂T-S模糊建模方法是有效的,它具有模糊模型的特点,可以任意精度逼近任何非线性系统,为柔性机械臂的模糊建模和下一步研究提供了理论指导及重要的前提条件.