采用DNA 遗传算法优化设计的TS模糊控制系统

基于生物 DNA的结构和遗传机理 ,提出一种新颖的基于 DNA编码方法的遗传算法。给出了DNA遗传算法的结构 ,讨论了遗传操作算子。为验证 DNA遗传算法的有效性 ,将其应用于 TS模糊控制系统的优化设计 ,仿真结果表明该算法具有较好的自学习能力。     

一类Takagi-Sugeno模糊控制器的自适应遗传优化设计

提出了一类Takagi-Sugeno模糊控制器的自适应遗传优化设计方法。采用实数编码方式,并由自适应交叉和变异概率来控制遗传操作,有效地提高了参数优化的精度和算法的寻优效率。在优化过程中引入对称性参数约束条件,大大减小了算法的搜索空间。将该算法用于倒立摆T-S模糊控制器的设计,实现了控制器参数的快速自动整定。仿真结果表明,获得的T-S模糊控制器具有优良的性能。     

一类不确定非线性系统自适应模糊滑模控制

针对一类带有未知外部扰动的不确定非线性系统,建立自适应模糊滑模控制器。基于Lyapunov稳定性理论,设计系统可调参数的自适应规则,控制器的设计过程中无需知道系统的具体模型及未知非线性函数的先验知识。数值仿真的结果也验证了该方法的有效性。     

非线性互联系统的分散混合自适应智能控制

针对一类高阶互联MIMO非线性系统，利用TS模糊系统和神经网络的通用逼近能力，在神经网络控制器中引入模糊基函数，提出一种分散混合自适应智能控制器设计的新方案．基于等价控制思想，设计分散自适应控制器，无需计算TS模型．通过对不确定项进行自适应估计，取消了其存在已知上界的假设．通过理论分析，证明了闭环智能控制系统所有信号有界，跟踪误差收敛到零．     

带有伸缩器和饱和器的一类非线性系统模糊自适应控制设计

本文针对一类带有未知齐次函数的非线性系统,首先基于伸缩器和饱和器的概念,将T-S型模糊逻辑系统的输入–输出进行改造而形成扩展模糊逻辑系统,然后利用扩展模糊逻辑系统给出一种带有可调伸缩因子参数的模糊自适应控制器的设计方法.由于该方法不依赖模糊规则数目,因而不仅能有效减少在线估计的参数数目,而且能够保证被控系统的状态一致终极有界.最后所给数值仿真算例说明了该设计方法的有效性.     

一类不确定非线性离散系统的模糊自适应控制器设计

针对一类不确定非线性离散系统,提出一种带有自动可调伸缩因子的模糊自适应控制方法.该控制器设计方法的优点是模糊逻辑系统的逼近精度不再依赖于模糊逻辑系统的结构和规则数目,参数自适应律调节与被逼近函数的特征和逼近精度有关,因此能有效减少在线估计的参数数目,且设计方法能够保证闭环系统的所有状态半全局一致终极有界.最后,通过数值仿真算例表明所提出方法的有效性.     

基于Pareto协同进化算法的TS糊模型设计

提出一种可同时构造多个精确性和解释性较好折中的TS模糊模型的设计方法.该方法由以下两步组成:1)采用模糊聚类算法辨识初始模型;2)利用Pareto协同进化算法对所获得的初始模型进行结构和参数优化.Pareto协同进化算法由规则前件种群和隶属函数种群组成, 其目标函数同时考虑模型的精确性和解释性,采用一种新的基于非支配排序的多种群合作策略.利用该方法对一类合成非线性动态系统进行建模,仿真结果验证了该方法的有效性.     

基于微分进化算法的模糊模型设计

提出一种基于微分进化算法的TS模糊模型设计方法。该方法利用“匹茨堡型”实数编码的微分进化算法,对初始模糊模型的结构和参数进行学习。微分进化算法的目标函数同时考虑模型的精确性和解释性。利用该方法进行一类合成非线性动态系统的辨识,仿真结果验证了该方法的有效性。     

非线性网络控制系统的故障检测

针对一类具有随机丢包的非线性网络控制系统,研究了系统的故障检测问题.基于T-S模糊模型将对象线性化,考虑了控制器和执行器之间、控制器和传感器之间的随机丢包现象,采用满足Bernoulli分布的二进制序列来描述数据传输的随机丢包.同时利用模糊主导子系统规则,设计了模糊观测器,给出了基于观测器闭环系统渐近稳定的充分条件,并通过数值仿真实验验证了该方法的有效性.     

基于混沌DNA遗传算法的模糊递归神经网络建模

本文受生物DNA分子遗传机制和混沌优化算法的启发,提出了一种混沌DNA遗传算法,用于优化T-S模糊递归神经网络（FRNN）.该方法使用碱基序列表示T-S模糊递归神经网络的前件部分参数,包括模糊规则数,隶属度函数中心点和宽度;设计更为复杂的遗传操作算子来改进遗传算法的寻优性能;利用混沌优化算法优化种群中的较差个体.同时使用递推最小二乘法（RLS）来辨识T-S模糊递归神经网络的后件部分参数.最后,采用基于混沌DNA遗传算法的T-S模糊递归神经网络对一种典型的pH中和过程进行建模。通过与其他建模方法的比较,仿真实验结果表明了所建模型的有效性.     

Emergence of self‐learning fuzzy systems by a new virus DNA–based evolutionary algorithm

In this article, we propose a new approach to the virus DNA–based evolutionary algorithm (VDNA‐EA) to implement self‐learning of a class of Takagi‐Sugeno (T‐S) fuzzy controllers. The fuzzy controllers use T‐S fuzzy rules with linear consequent, the generalized input fuzzy sets, Zadeh fuzzy logic and operators, and the generalized defuzzifier. The fuzzy controllers are proved to be nonlinear proportional‐integral (PI) controllers with variable gains. The fuzzy rules are discovered automatically and the design parameters in the input fuzzy sets and the linear rule consequent are optimized simultaneously by the VDNA‐EA. The VDNA‐EA uses the VDNA encoding method that stemmed from the structure of the VDNA to encode the design parameters of the fuzzy controllers. We use the frameshift decoding method of the VDNA to decode the DNA chromosome into the design parameters of the fuzzy controllers. In addition, the gene transfer operation and bacterial mutation operation inspired by a microbial evolution phenomenon are introduced into the VDNA‐EA. Moreover, frameshift mutation operations based on the DNA genetic operations are used in the VDNA‐EA to add and delete adaptively fuzzy rules. Our encoding method can significantly shorten the code length of the DNA chromosomes and improve the encoding efficiency. The length of the chromosome is variable and it is easy to insert and delete parts of the chromosome. It is suitable for complex knowledge representation and is easy for the genetic operations at gene level to be introduced into the VDNA‐EA. We show how to implement the new method to self‐learn a T‐S fuzzy controller in the control of a nonlinear system. The fuzzy controller can be constructed automatically by the VDNA‐EA. Computer simulation results indicate that the new method is effective and the designed fuzzy controller is satisfactory. © 2003 Wiley Periodicals, Inc.     

采用DNA进化算法优化设计TS模糊控制器

The DNA evolutionary algorithm(DNA-EA)and the DNA genetic algorithm(DNA-GA)based on a new DNA encoding method are propsed based on the structure and the genetic mechanism of biological DNA. The DNA-EA and the DNA-GA are applied into the optimal design of TS fuzzy control system. The simulation results show the effectiveness of the two DNA algorithms, excellent self-learning capability. However, the DNA-EA is superior to the DNA-GA in the simulation performance.     

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.     

Genetic reinforcement learning through symbiotic evolution forfuzzy controller design

An efficient genetic reinforcement learning algorithm for designing fuzzy controllers is proposed in this paper. The genetic algorithm (GA) adopted in this paper is based upon symbiotic evolution which, when applied to fuzzy controller design, complements the local mapping property of a fuzzy rule. Using this Symbiotic-Evolution-based Fuzzy Controller (SEFC) design method, the number of control trials, as well as consumed CPU time, are considerably reduced when compared to traditional GA-based fuzzy controller design methods and other types of genetic reinforcement learning schemes. Moreover, unlike traditional fuzzy controllers, which partition the input space into a grid, SEFC partitions the input space in a flexible way, thus creating fewer fuzzy rules. In SEFC, different types of fuzzy rules whose consequent parts are singletons, fuzzy sets, or linear equations (TSK-type fuzzy rules) are allowed. Further, the free parameters (e.g., centers and widths of membership functions) and fuzzy rules are all tuned automatically. For the TSK-type fuzzy rule especially, which put the proposed learning algorithm in use, only the significant input variables are selected to participate in the consequent of a rule. The proposed SEFC design method has been applied to different simulated control problems, including the cart-pole balancing system, a magnetic levitation system, and a water bath temperature control system. The proposed SEFC has been verified to be efficient and superior from these control problems, and from comparisons with some traditional GA-based fuzzy systems.     

A general technique for deriving analytical structure of fuzzy controllers using arbitrary trapezoidal input fuzzy sets and Zadeh AND operator

Deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding, insightful analysis, and more effective design of fuzzy control systems. We previously developed a technique for deriving the analytical structure of the fuzzy controllers that use Zadeh fuzzy AND operator and the symmetric, identical trapezoidal or triangular input fuzzy sets. Many fuzzy controllers use arbitrary trapezoidal/triangular input fuzzy sets that are asymmetric. At present, there exists no technique capable of deriving the analytical structure of these fuzzy controllers. Extending our original technique, we now present a novel method that can accomplish rigorously the structure derivation for any fuzzy controller, Mamdani type or TS type, that employs the arbitrary trapezoidal input fuzzy sets and Zadeh fuzzy AND operator. The new technique contains our original technique as a special case. Given the importance of PID control, we focus on Mamdani fuzzy PI and PD controllers in this paper and show in detail how to use the new technique for different configurations of the fuzzy PI/PD controllers. The controllers use two arbitrary trapezoidal fuzzy sets for each input variable, four arbitrary singleton output fuzzy sets, four fuzzy rules, Zadeh fuzzy AND operator, and the centroid defuzzifier. This configuration is more general and complicated than the Mamdani fuzzy PI/PD controllers in the current literature. It actually contains them as special cases. We call this configuration the generalized fuzzy PI/PD controller.     

Sufficient conditions on uniform approximation of multivariatefunctions by general Takagi-Sugeno fuzzy systems with linear ruleconsequent

We have constructively proved a general class of multi-input single-output Takagi-Sugeno (TS) fuzzy systems to be universal approximators. The systems use any types of continuous fuzzy sets, fuzzy logic AND, fuzzy rules with linear rule consequent and the generalized defuzzifier. We first prove that the TS fuzzy systems can uniformly approximate any multivariate polynomial arbitrarily well, and then prove they can also uniformly approximate any multivariate continuous function arbitrarily well. We have derived a formula for computing the minimal upper bounds on the number of fuzzy sets and fuzzy rules necessary to achieve the prespecified approximation accuracy for any given bivariate function. A numerical example is furnished. Our results provide a solid-theoretical basis for fuzzy system applications, particularly as fuzzy controllers and models     

Constructing nonlinear variable gain controllers via theTakagi-Sugeno fuzzy control

We investigated the analytical structure of the Takagi-Sugeno (TS) type of fuzzy controllers, which was unavailable in the literature. The TS fuzzy controllers we studied employ a new and simplified TS control rule scheme in which all the rule consequent use a common function and are proportional to one another, greatly reducing the number of parameters needed in the rules. Other components of the fuzzy controllers are general: arbitrary input fuzzy sets, any type of fuzzy logic, and the generalized defuzzifier, which contains the popular centroid defuzzifier as a special case. We proved that all these TS fuzzy controllers were nonlinear variable gain controllers and characteristics of the gain variation were parametrized and governed by the rule proportionality. We conducted an in-depth analysis on a class of nonlinear variable gain proportional-derivative (PD) controllers. We present the results to show: (1) how to analyze the characteristics of the variable gains in the context of control; (2) why the nonlinear variable gain PD controllers can outperform their linear counterpart; and (3) how to generate various gain variation characteristics through the manipulation of the rule proportionality     

Control of Underactuated Manipulators using Fuzzy Logic Based Switching Controller

This paper introduces a new concept for designing a fuzzy logic based switching controller in order to control underactuated manipulators. The proposed controller employs elemental controllers, which are designed in advance. Parameters of both antecedent and consequent parts of a fuzzy indexer are optimized by using evolutionary computation, which is performed off-line. Design parameters of the fuzzy indexer are encoded into chromosomes, i.e., the shapes of the Gaussian membership functions and corresponding switching indices of the consequent part are evolved to minimize the angular position errors. Such parameters are trained for different initial configurations of the manipulator and the common rule base is extracted. Then, these trained fuzzy rules can be brought into the online operations of underactuated manipulators. 2-DOF underactuated manipulator is taken into consideration so as to illustrate the design procedure. Computer simulation results show that the new methodology is effective in designing controllers for underactuated robot manipulators.     

基于TS模型的二型模糊控制器和观测器分析与设计

主要探讨一种新的系统方法——二型模糊系统在控制上的应用．文章先介绍了二型模糊集合和系统的基本概念和基本方法，然后集中推导TS模型下规则的输出形式，推广一型系统的特性，从而获得二型模糊控制器和观测器的表达式、稳定性以及其它特性分析方法，并以小车倒立摆仿真验证．最后文章从整体上分析和比较了传统系统、一型模糊系统和二型模糊系统的主要特点和不同点．     

General SISO Takagi-Sugeno fuzzy systems with linear ruleconsequent are universal approximators

Takagi-Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzzy controllers and models, “Are TS fuzzy systems with linear rule consequent universal approximators?” If the answer is yes, then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration? In this paper, we provide answers to these questions for a general class of single-input single-output (SISO) fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We first constructively prove that this general class of SISO TS fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove, by utilizing the Weierstrass approximation theorem, that the general TS fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision. Furthermore, we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound, An illustrative numerical example is provided