一种等价于PI的二型模糊控制器设计算法

区间二型模糊集合将次隶属度做了简化,基于KM降阶算法的区间二型模糊控制器实现起来相对简单。虽然区间二型模糊控制器在一定程度上优于传统的一型模糊控制器或者PI控制器等,但区间二型模糊控制器并没有充分利用二型模糊集合的次隶属度信息。为解决这些问题,研究了普通二型模糊控制器的一般结构,提出了一种等价于PI的二型模糊控制器。该控制器基于普通二型模糊集合的α平面表现形式,在次隶属度函数的顶点处,将区间二型模糊集合简化为一型模糊集合。通过n阶有自平衡对象,无自平衡对象以及2个非线性对象的仿真结果表明,提出的二型模糊控制器能够得到较好的控制效果。     

基于NT降阶的乘积型区间二型模糊控制器结构分析

目前区间二型模糊控制器的结构分析主要基于Zadeh的取小推理和KM降阶算法。KM算法是一循环迭代过程,没有解析解,无法进行控制器的稳定性分析,且取小推理需要进行输入空间的划分,过程较为繁琐。提出了一种简化的区间二型模糊控制器分析方法,该方法首先采用乘积推理,模糊规则的激发隶属度为输入变量隶属度的乘积,统一了控制器的表达式形式,避免了输入空间的划分过程,模糊控制器的结构分析更加简单。二型模糊集合采用NT降阶算法,该算法直接利用首隶属度函数的上、下限的平均值来进行解模糊化操作,避免了迭代计算,简化了降阶过程。控制器的表达式等效于一个增量式PI（位置式PD）控制器,其比例增益、积分增益以及补偿项均为非线性可调。而且还能得到控制器的闭环表达式,易于进行区间二型模糊控制器的稳定性分析与设计等。     

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。     

一类乘积型区间二型模糊控制器的解析结构

区间二型模糊控制器的降型算法需要使用迭代计算,是导致其解析结构推导困难的主要原因.针对乘积型区间二型模糊控制器,本文提出了一种新的解析结构推导方法.区间二型模糊控制器的配置为:三角形输入模糊集,一型输出模糊单值,集合中心法降型器,平均法解模糊器和基于乘积型"与"操作的规则前件.通过对比传统PID控制器的解析结构,证明了区间二型模糊控制器等效于两个PI(或PD)控制器之和.利用KM算法的迭代终止条件,提出了6步骤IC划分法,保证了激活子空间的正确划分.叠加各个子空间,即可得出全局IC划分图.为了避免重复求解符号数学方程,提出了IC边界线的直接定义法,改进了6步骤IC划分法的便利性.本文方法避开了降型算法的迭代计算,可以保证推导出区间二型模糊控制器的闭环解析表达式.     

一种新的区间二型模糊集合降阶算法

区间二型模糊集合的KM/EKM降阶算法,其效率较低,难以用于二型模糊逻辑的实时控制。而基于切换点计算公式的单调性关系的IASC和EIASC算法虽然其运算时间低于KM/EKM,但其初始值都是从两侧端点开始,其效率也有待提高。本文提出了一种新的二型模糊集合降阶算法,利用切换点计算公式和论域中值的关系以及初始化左右切换点的值来提高计算效率,2个仿真实例验证了本文算法的有效性和实用性。     

基于加权Karnik-Mendel算法的区间二型模糊逻辑系统降型

二型模糊逻辑系统是当前的学术研究的热点问题,而降型是该系统中非常重要的一个模块.Kamik-Mendel(KM)算法是被用来计算和完成区间二型模糊逻辑系统降型的标准算法.通过比较离散版本KM算法中求和运算和连续版本的KM(continuous version ofKM,CKM)算法中求积分运算,本文利用数值积分技术中牛顿-柯斯特求积公式将标准KM算法扩展成3种不同形式的加权KM(weighted KM,WKM)算法.而KM算法只是WKM算法中的一种特殊情况.3个计算机仿真例子用来阐述和分析WKM算法的表现,与传统的KM算法相比,WKM算法有较小的绝对误差和较快的收敛速度,给二型模糊逻辑系统设计者和应用者提供了潜在的应用价值.     

区间二型模糊逻辑系统质心降型及加权Nie-Tan算法

降型是二型模糊逻辑系统中的核心模块。Nie-Tan (NT) 算法不涉及到迭代过程,可直接得到系统输出,具有减少计算消耗的优势,而连续NT(CNT)算法在最近的研究中被证明为准确的质心降型算法。通过分析离散NT算法中求和运算和连续NT算法中的求积分运算,利用数值积分技术中牛顿-柯斯特求积公式将NT算法扩展成3种不同形式的加权NT（WNT）算法。在取相同的主变量采样率的情况下,3个计算机仿真例子表明了WNT算法比NT算法有更小的绝对误差且计算速度几乎相同,这使3种不同形式的WNT算法在区间二型模糊逻辑系统的实时应用上具有潜在的可行性和有效性。     

一种改进的区间二型模糊控制器设计

针对二型模糊控制器设计中出现的降型计算方法损失不确定性信息的问题,提出一种改进的区间二型模糊控制器．该控制器在充分利用二型模糊推理结果的前提下,对区间模糊输出进行再次优化,其优化指标可直接与被控系统性能相关,由此可得到更有利于提高系统整体性能的准确输出量．最后,将改进的控制器用于汽车非线性悬架系统的控制,仿真结果验证了所提出方法的有效性．     

线性不确定系统的给定阶最优控制器设计

为避免间接法设计降阶控制器的模型近似引起的性能下降,本文在静态输出反馈控制器设计的基础上,直接设计了线性不确定系统的给定阶混合H2/H∞动态反馈控制器.利用系统内外分解方法,得到了最优降阶状态观测器.通过求解降维状态观测器的静态输出反馈,可得到降阶控制的最优反馈增益阵.给定阶控制器由两个Ric cati方程和一个Lyapunov方程参数化表示.最后,通过一个例子,说明了本文提出的给定阶控制器设计方法.     

广义二型模糊逻辑系统降型及其采样离散Nie-Tan算法

广义二型模糊逻辑系统在近年来成为学术研究的热点问题,而降型是该系统中的核心模块。最近的研究证明了连续Nie-Tan(CNT)算法是计算区间二型模糊集质心的准确方法。发现了离散Nie-Tan(NT)算法中的求和运算和CNT算法中的求积分运算的内在联系,用2类算法完成基于广义二型模糊集α-平面表达理论的广义二型模糊逻辑系统质心降型。3个计算机仿真实验表明,当适当增加主变量采样点个数时,所提出的基于主变量采样的离散NT算法计算出的广义二型模糊逻辑系统质心降型集和解模糊化值结果可以精确地逼近基准的CNT算法,且采样离散NT算法的计算效率远远高于CNT算法的效率。     

Design of interval type-2 fuzzy sliding-mode controller

In this paper, an interval type-2 fuzzy sliding-mode controller (IT2FSMC) is proposed for linear and nonlinear systems. The proposed IT2FSMC is a combination of the interval type-2 fuzzy logic control (IT2FLC) and the sliding-mode control (SMC) which inherits the benefits of these two methods. The objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the interval type-2 fuzzy sliding-mode controller system. The design procedure of the IT2FSMC is explored in detail. A typical second order linear interval system with 50% parameter variations, an inverted pendulum with variation of pole characteristics, and a Duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method. The simulation results show that the IT2FSMC achieves the best tracking performance in comparison with the type-1 Fuzzy logic controller (T1FLC), the IT2FLC, and the type-1 fuzzy sliding-mode controller (T1FSMC).     

二型模糊相似度及其应用

二型模糊集可以直接处理高度不确定性,并且具有很强的实际应用背景。基于二型模糊相似度的公理化定义,给出了新的二型模糊相似度计算公式。进一步,将二型模糊相似度与Yang-Shih方法相结合,用于二型模糊数据的聚类分析,聚类结果与Yang-Lin的结果进行了比较,实例表明新的相似度更合理。此外,基于二型模糊相似度,讨论了二型模糊信息系统的属性约简问题,给出了相应约简的分辨函数法,并通过实例说明了该方法的具体计算步骤。     

基于包含度的区间二型模糊粗糙集

基于区间二型模糊包含度的公理化定义,给出了新的区间二型模糊包含度计算公式.进一步,通过包含度定义了区间二型模糊粗糙集,并讨论了它的一些基本性质.最后,利用区间二型模糊粗糙集研究了连续域决策信息系统的属性约简,给出了新的约简方法.实例说明了该约简方法的具体计算步骤,并且通过实验验证了该算法的有效性和可行性.     

Distinguishability of interval type-2 fuzzy sets data by analyzing upper and lower membership functions

In this paper, we deal with the problem of classification of interval type-2 fuzzy sets through evaluating their distinguishability. To this end, we exploit a general matching algorithm to compute their similarity measure. The algorithm is based on the aggregation of two core similarity measures applied independently on the upper and lower membership functions of the given pair of interval type-2 fuzzy sets that are to be compared. Based on the proposed matching procedure, we develop an experimental methodology for evaluating the distinguishability of collections of interval type-2 fuzzy sets. Experimental results on evaluating the proposed methodology are carried out in the context of classification by considering interval type-2 fuzzy sets as patterns of suitable classification problem instances. We show that considering only the upper and lower membership functions of interval type-2 fuzzy sets is sufficient to (i) accurately discriminate between them and (ii) judge and quantify their distinguishability.     

Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities

This paper presents an indirect approach to interval type-2 fuzzy logic system modeling to forecaste the level of air pollutants. The type-2 fuzzy logic system permits us to model the uncertainties among rules and the parameters related to data analysis. In this paper, we propose an indirect method to create an interval type-2 fuzzy logic system from a historical data, where Footprint of Uncertainties of fuzzy sets are extracted by implementation of an interval type-2 FCM algorithm and based on an upper and lower value for the level of fuzziness m in FCM. Finally, the proposed model is applied for prediction of carbon monoxide concentration in Tehran air pollution. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to type-1 fuzzy logic systems in terms of two performance indices.     

Observer-based method for synchronization of uncertain fractional order chaotic systems by the use of a general type-2 fuzzy system

Synchronization of the fractional order chaotic systems is extensively studied in recent years due to its potential applications in many branches of science and engineering. The main problems in this field are that the dynamics of the system in hand are often uncertain and are perturbed by external disturbances. Also the unknown nonlinear functions in the system dynamics are generally complicated and in many practical applications we have measurement errors and unavailable states. In this paper, a novel robust and asymptotically stable controller is proposed to synchronize uncertain fractional order chaotic systems. Its design is based on linear matrix inequality (LMI) technique. Furthermore, an observer is presented to estimate the unavailable states. A general type-2 fuzzy system (GT2FS) based on α-plane representation with Gaussian secondary membership functions (MF) and type-2 non-singleton fuzzification is proposed to approximate the unknown complex nonlinear functions in the dynamics of system. The input uncertainties associated with the observer error and the malfunctioning of the input devices are modeled by interval type-2 fuzzy MFs instead of crisp numbers. To decrease the computational cost of the GT2FS, a simple type-reduction method is proposed. The antecedent parameters of GT2FS are tuned based on a modified form of social spider optimization (SSO) algorithm. The simulation examples show that the proposed control scheme gives high performance in the presence of unknown functions, external disturbances and unavailable states. The performance of GT2FS with different α-levels and different fuzzification methods are compared with type-1 and interval type-2 fuzzy systems in several examples.     

State feedback control of interval type-2 Takagi–Sugeno fuzzy systems via interval type-2 regional switching fuzzy controllers

The interval type-2 Takagi–Sugeno fuzzy systems have been proposed to handle nonlinear systems subject to parameter uncertainties. In this paper, a new type of state feedback controller, namely, interval type-2 regional switching fuzzy controller, is proposed to conceive less-conservative stabilisation conditions, which is switched by basing on the values of system states. To further reduce the conservativeness in the stability analysis, the information of lower and upper membership functions is also considered. Stability conditions for the interval type-2 fuzzy closed-loop systems are presented in the form of linear matrix inequalities (LMIs). Simulation examples are provided to illustrate the effectiveness of the proposed method.