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。     

基于遗传算法的广义Takagi-Sugeno模糊逻辑系统最优参数辨识

针对Takagi-Sugeno模糊逻辑系统的隶属函数不具有自适应性且模糊规则数的确定 带有很大的人为主观性,这里引入了一类广义Takagi-Sugeno模糊逻辑系统;在模型实现上，以 广义Takagi-Sugeno模型为个体,采用简单、有效的矩阵编码方式,借助遗传算法得到一个次优 的广义Takagi-Sugeno模糊系统模型,该模型不仅能很好地逼近所要辨识的非线性系统,而且 还具有较低的复杂度.仿真结果表明了广义Takagi-Sugeno模型及其参数辨识方法的正确性和 有效性.     

复杂系统的递阶模糊辨识

针对Takagi_Sugeno模糊模型 (T_S模型 )严重的维数灾问题, 借鉴GMDH算法, 提出了一种新的复杂系统递阶模糊辨识方法. 本文首先详细描述了由两输入变量的特殊T_S模型所组成的递阶模糊模型 ;然后提出了具体的辨识该递阶模糊模型的方法. 该方法的特点是 :a)在结构辨识阶段, 用FCM模糊聚类方法评价系统中每个输入变量的重要性, 以便构造合理的递阶模糊模型 ;b)预先合理地确定了所要辨识的参数的初始值, 用扩展卡尔曼滤波方法可很快地得到这些参数. 最后, 给出的仿真实例说明了本文辨识方法的有     

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．     

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.     

一种简化的区间二型模糊系统辨识方法

KM降阶算法是目前区间二型模糊集合常用的降阶算法,针对其效率低、难以用于实时辨识与控制的缺点,提出了一种简化的区间二型模糊系统辨识方法。该方法采用二型T-S模糊模型,前件参数为区间二型模糊集合,后件参数为普通T-S模糊模型形式。二型T-S模糊模型的解模糊化采用简化的降阶算法,提高了模型的辨识效率,可用于实时辨识与控制。仿真实例表明,所提算法在不降低辨识精度的情况下能够有效提高辨识效率。     

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.     

参考模糊集合构造方法及模糊模型辨识

本文提出了一种基于参考模糊集的模糊模型辨识方法,探讨了模型结构和模糊关系的辨识问题.在隶属函数的定义上引入了优化算法,最终将辨识问题转化为优化问题.文中给出了具体的辨识算法,仿真实例表明该模型辨识方法具有满意的精度.     

基于模糊似然函数的模糊辨识方法

提出一种基于模糊似然函数的模糊辨识方法。该方法利用模糊似然函数对样本数据进行聚类，并使模糊模型的结构辨识和参数辨识能同时完成，从而实现模糊模型的在线辨识。仿真结果证明了该方法的有效性。     

Exact analytical inverse mapping of decomposable TS fuzzy systems with singleton and linear consequents

In this study, a new method is proposed for the exact analytical inverse mapping of Takagi–Sugeno fuzzy systems with singleton and linear consequents where the input variables are described by using strong triangular partitions. These fuzzy systems can be decomposed into several fuzzy subsystems. The output of the fuzzy subsystem results in multi-linear form in singleton consequent case or multi-variate second order polynomial form in linear consequent case. Since there exist explicit analytical formulas for the solutions of first and second order equations, the exact analytical inverse solutions can be obtained for decomposable Takagi–Sugeno fuzzy systems with singleton and linear consequents. In the proposed method, the output of the fuzzy subsystem is represented by using the matrix multiplication form. The parametric inverse definition of the fuzzy subsystem is obtained by using appropriate matrix partitioning with respect to the inversion variable. The inverse mapping of each fuzzy subsystem can then easily be calculated by substituting appropriate parameters of the fuzzy subsystem into this parametric inverse definition. So, it becomes very easy to find the analytical inverse mapping of the overall Takagi–Sugeno fuzzy system by composing inverse mappings of all fuzzy subsystems. The exactness and the effectiveness of the proposed inversion method are demonstrated on trajectory tracking problems by simulations.     

Robust fuzzy stabilisation of interval plants

The paper deals with the problem of stabilisation of interval systems. To this end, by using Takagi–Sugeno fuzzy mechanism, a Mamdani-type PID-like fuzzy controller is modified and extended to develop a new PID-like Takagi–Sugeno fuzzy stabilising controller for the plant described by an interval system. Indeed, a PID-like Takagi–Sugeno fuzzy controller and an interval plant are considered in the forward path of a unity feedback system, and parameters in Takagi–Sugeno fuzzy controller are determined so that the stability of the closed-loop system is assured. The closed-loop system has a multilinear uncertainty structure. Therefore, based on the Zero Exclusion Condition for multilinear uncertain systems, a new theorem presenting sufficient conditions for the Takagi–Sugeno fuzzy controller to be robust stability guaranteed is also derived. An example is given to illustrate the application and the effectiveness of the proposed controller.     

T–S fuzzy model with nonlinear consequence and PDC controller for a class of nonlinear control systems

In this paper a new Takagi–Sugeno (T–S) fuzzy model with nonlinear consequence (TSFMNC) is presented which can approximate a class of smooth nonlinear systems, nonlinear dynamical systems and nonlinear control systems. It is also proved that Takagi–Sugeno fuzzy controller with nonlinear consequence (TSFCNC) can be used to approximate a class of nonlinear state-feedback controllers using the so-called parallel distributed compensation (PDC) method. The inverted pendulum problem has been simulated with TSFCNC and compared with Takagi–Sugeno fuzzy controller with linear consequence (TSFCLC) and the results show that TSFCNC performs better than TSFCLC. A real-life example of dynamic positioning of ship is simulated and the results also show that TSFCNC performs better than TSFCLC.     

A new approach to fuzzy modeling

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm     

Exponential H∞ stable learning method for Takagi–Sugeno fuzzy delayed neural networks: A convex optimization approach

In this paper, we propose some new results on stability for Takagi–Sugeno fuzzy delayed neural networks with a stable learning method. Based on the Lyapunov–Krasovskii approach, for the first time, a new learning method is presented to not only guarantee the exponential stability of Takagi–Sugeno fuzzy neural networks with time-delay, but also reduce the effect of external disturbance to a prescribed attenuation level. The proposed learning method can be obtained by solving a convex optimization problem which is represented in terms of a set of linear matrix inequalities (LMIs). An illustrative example is given to demonstrate the effectiveness of the proposed learning method.     

Supervision of nonlinear adaptive controllers based on fuzzy models

A novel approach for the supervision of fuzzy model on-line adaptation is proposed. A nonlinear predictive controller is designed based on a Takagi–Sugeno fuzzy model. By adapting the fuzzy model on-line, high control performance can be achieved even with time-variant process behaviour and changing unmodelled disturbances. A local weighted recursive least-squares algorithm exploits the local linearity of Takagi–Sugeno fuzzy models. In order to cope with problems resulting from insufficient excitation, a supervisory level is introduced. It comprises a variable forgetting factor and an additional adaptation model which makes the on-line adaptation robust and reliable. The effectiveness and real-world applicability of the proposed approach are demonstrated by application to temperature control of a heat exchanger.     

竞争式Takagi-Sugeno模糊再励学习

针对连续空间的复杂学习任务,提出了一种竞争式Takagi-Sugeno模糊再励学习网络 (CTSFRLN),该网络结构集成了Takagi-Sugeno模糊推理系统和基于动作的评价值函数的再 励学习方法.文中相应提出了两种学习算法,即竞争式Takagi-Sugeno模糊Q-学习算法和竞争 式Takagi-Sugeno模糊优胜学习算法,其把CTSFRLN训练成为一种所谓的Takagi-Sugeno模 糊变结构控制器.以二级倒立摆控制系统为例,仿真研究表明所提出的学习算法在性能上优于 其它的再励学习算法.     

Fault Diagnosis and Sliding Mode Fault Tolerant Control for Non‐Gaussian Stochastic Distribution Control Systems Using T‐s Fuzzy Model

For the non‐Gaussian stochastic distribution control system using Takagi‐Sugeno fuzzy model, a new fault diagnosis and sliding mode fault tolerant control algorithm is presented. First, a new adaptive fault diagnosis algorithm is adopted to diagnose the fault that occurred in the system, and the observation error system is proven to be uniformly bounded. Second, the sliding mode control algorithm is used to reconfigure the controller, based on the fault estimation information. The post‐fault probability density function can still track the given distribution, leading to fault tolerant control of non‐Gaussian stochastic distribution control systems using Takagi‐Sugeno fuzzy model. Finally, simulation results show the effectiveness of the proposed method.     

时滞Hopfield神经网络的随机稳定性分析

T-S模型提供了一种通过模糊集和模糊推理将复杂的非线性系统表示为线性子模型的方法。研究了时滞Hopfield神经网络的随机稳定性（SFVDHNNs）。首先描述了SFVDHNNs模型,然后用Lyapunov方法研究了SFVDHNNs全局均方指数稳定性,通过可以被一些标准的数值分析方法求解的线性矩阵不等式（LMIs）得出了稳定性标准。     

LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form

This paper presents the stabilization analysis for a class of nonlinear systems that are represented by a Takagi and Sugeno (TS) discrete fuzzy model (Takagi and Sugeno IEEE Trans. Systems Man Cybern. 15(1)(1985)116). The main result given here concerns their stabilization using new control laws and new nonquadratic Lyapunov functions. New relaxed conditions and linear matrix inequality-based design are proposed that allow outperforming previous results found in the literature. Two examples are also provided to demonstrate the efficiency of the approaches.