Robust H ∞ reliable control of time delay nonlinear systems via Takagi–Sugeno fuzzy models

This article is focused on reliable fuzzy H _∞ controller design for a class of Takagi–Sugeno (T–S) fuzzy systems with state delay, actuator failures, disturbance input and norm bounded uncertainties. In the design, the H _∞ performance of the closed-loop system is optimised during normal operation (without failures) while the system satisfies a prescribed H _∞ performance level in the case of actuator failures. Two methods are presented in this study. In the first method, delay-dependent conditions are derived based on a single Lyapunov–Krasovskii function. This method improves delay-independent results existing in the literature. Next, to further reduce the conservatism, we use a parameter-dependent Lyapunov–Krasovskii function. The new sufficient conditions for the existence of the suboptimal robust reliable controller are shown in terms of linear matrix inequalities (LMIs), which can be solved by using LMI optimisation techniques. A simulation example shows the effectiveness of the proposed methods.     

广义Sugeno模糊积分的次线性性

在给定的K-拟可加模糊测度空间上,借助于引进新拟乘法算子""给出了广义Sugeno模糊积分定义,依据拟加法和拟乘法定义及运算性质,研究了这种广义Sugeno模糊积分的次可加性乃至次线性性,从而进一步丰富了模糊积分的理论。     

Hydraulic turbine governing system identification using T–S fuzzy model optimized by chaotic gravitational search algorithm

Hydraulic turbine governing system (HTGS) is a complicated nonlinear system that controls the frequency and power output of hydroelectric generating unit (HGU). The modeling of HTGS is an important and difficult task, because some components, like hydraulic turbine and governor actuator, are with strong nonlinearity. In this paper, a novel Takagi–Sugeno (T–S) fuzzy model identification method based on chaotic gravitational search algorithm (CGSA) is proposed and applied in the modeling of HTGS. In the proposed method, fuzzy c-regression model clustering algorithm is used to partition the input space and identify the coarse antecedent membership function (MF) parameters at first. And then, a novel CGSA is proposed to search better MF parameters around the coarse results, in which chaotic search has been embedded in the iteration of basic GSA to search and replace the current best solution of GSA. The performance of the proposed fuzzy model identification method is validated by benchmark problems, and the results show that the accuracies of identified models have been improved significantly compared with the other existing models. Finally, the proposed approach has been applied to approximate the dynamic behaviors of HTGS of a HGU in a hydropower station of Jiangxi Province of China. The experimental results show that our approach can identify the HTGS satisfactorily with acceptable accuracy.     

An Analytical Study on Structure, Stability and Design of General Nonlinear Takagi–Sugeno Fuzzy Control Systems

In this paper, we first study analytical structure of general nonlinear Takagi-Sugeno (TS, for short) fuzzy controllers, then establish a condition for analytically determining asymptotic stability of the fuzzy control systems at the equilibrium point, and finally use the stability condition in design of the control systems that are at least locally stable. The general TS fuzzy controllers use arbitrary input fuzzy sets, any types of fuzzy logic AND, TS fuzzy rules with linear consequent and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case. We have mathematically proved that the general TS fuzzy controllers are nonlinear controllers with variable gains continuously changing with controllers’ input variables. Using Lyapunov’s linearization method, we have established a necessary and sufficient condition for analytically determining local asymptotic stability of TS fuzzy control systems, each of which is made up of a fuzzy controller of the general class and a nonlinear plant. We show that the condition can be used in practice even when the plant model is not explicitly known. We have utilized the stability condition to design, with or without plant model, general TS fuzzy control systems that are at least locally stable. Three numerical examples are given to illustrate in detail how to use our new results. Our results offer four important practical advantages: (1) our stability condition, being a necessary and sufficient one, is the tightest possible stability condition, (2) the condition is simple and easy to use partially because it only needs the fuzzy controller structure around the equilibrium point, (3) the condition can be used for determining system local stability and designing fuzzy control systems that are stable at least around the equilibrium point even when the explicit plant models are unavailable, and (4) the condition covers a very broad range of nonlinear TS fuzzy control systems, for which a meaningful global stability condition seems impossible to establish.     

基于DSP的实时T-S型模糊控制器设计及其在直流无刷电机控制中的应用

提出了一种简化模糊控制算法，它通过把系统的输入输出空间划分为一个完备的模糊模式集，且寻找与实时输入对应的模糊模式，对整个系统进行了简化；在此基础上，设计了以数字信号处理器(DSP)为核心的模糊控制器；描述了其在直流无刷电机控制中的应用。实验结果表明，该模糊控制器具有实时性强、响应速度快、精度高的特点。     

A new evolving compact optimised Takagi–Sugeno fuzzy model and its application to nonlinear system identification

A new encoding scheme is presented for a fuzzy-based nonlinear system identification methodology, using the subtractive clustering and non-dominated sorting genetic algorithm. The proposed method consists of two parts. The first part is related to the selection of most relevant or influencing inputs to the system and the second one is related to the tuning of fuzzy rules and parameters of the membership functions. The main purpose of the proposed scheme is to reduce the complexity and increase the accuracy of the model. In particular, three objectives are considered in the process of optimisation, namely, the number of inputs, number of rules and the root mean square of the modelling error. The performance of the developed method is validated by identifying the Box–Jenkins nonlinear benchmark system, and to the modelling of the forward and inverse dynamic behaviours of a magneto-rheological (MR) damper. The latter is also a challenging problem due to the inherent hysteretic and highly nonlinear dynamics of the MR damper. It is shown that the developed evolving Takagi–Sugeno (T–S) fuzzy model can identify and grasp the nonlinear dynamics of both systems very well, while a small number of inputs and fuzzy rules are required for this purpose.     

基于Takagi-Sugeno的再励学习模糊神经网络控制

提出一种模糊神经网络的自适应控制方案。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,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。相应地,提出了一种优化学习算法,其把竞争式Takagi-Sugeno模糊再励学习网络训练成为一种所谓的Takagi-Sugeno模糊变结构控制器。以一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。     

基于数值型数据的模糊规则快速挖掘方法

针对数值型数据能准确反应现实世界,但难以理解的问题,为了从数值型数据中挖掘出易于理解的知识,提出了基于数值型数据的模糊规则快速挖掘方法。该方法能从数值型数据中挖掘出一个零阶的Sugeno模糊规则,并采用一种启发式方法将这个零阶的Sugeno模糊规则的数值结论转变为两个带置信度的语言变量,并给出了规则库的存储结构。最后通过实例证明了这种快速模糊规则挖掘方法能避免复杂的数值型计算和能有效逼近非线性函数的优点．     

Pettis-Sugeno integral

0　ＩＮＴＲＯＤＵＣＴＩＯＮＦｕｚｚｙｍｅａｓｕｒｅａｎｄｆｕｚｚｙｉｎｔｅｇｒａｌｓｗｅｒｅｉｎｔｒｏ ｄｕｃｅｄｂｙＳｕｇｅｎｏ[1] ｔｏｅｖａｌｕｔｅｎｏｎ ａｄｄｉｔｉｖｅｏｒｎｏｎ ｌｉｎ ｅａｒｑｕａｎｔｉｔｙｉｎｓｙｓｔｅｍｓｅｎｇｉｎｅｅｒｉｎｇ .ＴｈｅＰｅｔｔｉｓｉｎｔｅ ｇｒａｌｈａｓｂｅｅｎｄｅｅｐｌｙｓｔｕｄｉｅｄｉｎｆｕｎｃｔｉｏｎａｌａｎａｌｙ ｓｉｓ[2 ,3] ,ｓｏｉｔｉｓｎａｔｕｒａｌｔｏａｓｋｗｈｅｔｈｅｒｗｅｃａｎｅｓｔａｂ ｌｉｓｈｂｙｕｓｉｎｇａｆｕｚｚｙｍｅａｓｕｒｅ…     

Efficient impulse noise removal using hybrid neuro-fuzzy filter with optimized intelligent water drop technique

Impulse noise (IN) affects the digital image, during transmission, digital storage, and image acquisition. IN removal from an image is necessary as it retains the quality of the image. This work concentrates on the IN. A neuro-fuzzy (NF) system based on a fuzzy technique which is trained by a learning algorithm derived from neural network theory was implemented for the removal of noise. A NF network for noise filtering in grayscale images that combines two NF filters with a postprocessor to produce the output was presented. However, Sugeno-type is not intuitive technique and it also less accurate. To overcome these problems, a hybrid NF filter with optimized intelligent water drop (IWD) technique is introduced, where hybridized Sugeno–Mamdani-based fuzzy interference system is implemented in both the NF filters to obtain more efficient noise removal system. To improve the accuracy of the assignment of membership values to each input pixels, the optimized IWD technique is utilized, as the choice of membership function decides the efficiency of the noise removal in the images. Here, Fuzzy rules have been used to obtain the filtered output. The Hybrid method maintains the accuracy of the Sugeno model and also the interpretable capability of the Mamdani model. This method is robust against the IN and it is flexible, efficient, and accurate than existing filtering method in both noise attenuation and detail preservation and it has a great scope for better real-time applications.