Hybrid compensation control for affine TSK fuzzy control systems

The paper proposes a way of designing state feedback controllers for affine Takagi-Sugeno-Kang (TSK) fuzzy models. In the approach, by combining two different control design methodologies, the proposed controller is designed to compensate all rules so that the desired control performance can appear in the overall system. Our approach treats all fuzzy rules as variations of a nominal rule and such variations are individually dealt with in a Lyapunov sense. Previous approaches have proposed a similar idea but the variations are dealt with as a whole in a robust control sense. As a consequence, when fuzzy rules are distributed in a wide range, the stability conditions may not be satisfied. In addition, the control performance of the closed-loop system cannot be anticipated in those approaches. Various examples were conducted in our study to demonstrate the effectiveness of the proposed control design approach. All results illustrate good control performances as desired.     

基于模糊神经网络的统一潮流控制器

为了减少先验知识对统一潮流控制器中模糊规则的设计和电力系统参数的变化对统一潮流控制器性能的影响,文中采用模糊神经网络来设计统一潮流控制器.为此首先简单介绍了统一潮流控制器的控制策略,然后阐述了自组织模糊神经网络和基于遗传算法的模糊神经网络的构造方法,接着将自组织模糊神经网络、基于遗传算法的模糊神经网络结合统一潮流控制器的控制策略应用于两种统一潮流控制器.最后通过MATLAB仿真例子来验证:这两种统一潮流控制器的设计方法的有效性.     

Fuzzy rule interpolation for multidimensional input spaces with applications: a case study

Fuzzy rule based systems have been very popular in many engineering applications. However, when generating fuzzy rules from the available information, this may result in a sparse fuzzy rule base. Fuzzy rule interpolation techniques have been established to solve the problems encountered in processing sparse fuzzy rule bases. In most engineering applications, the use of more than one input variable is common, however, the majority of the fuzzy rule interpolation techniques only present detailed analysis to one input variable case. This paper investigates characteristics of two selected fuzzy rule interpolation techniques for multidimensional input spaces and proposes an improved fuzzy rule interpolation technique to handle multidimensional input spaces. The three methods are compared by means of application examples in the field of petroleum engineering and mineral processing. The results show that the proposed fuzzy rule interpolation technique for multidimensional input spaces can be used in engineering applications.     

A novel fuzzy logic system based on N-version programming

For the consideration of different application systems, modeling the fuzzy logic rule, and deciding the shape of membership functions are very critical issues due to they play key roles in the design of fuzzy logic control system. This paper proposes a novel design methodology of fuzzy logic control system using the neural network and fault-tolerant approaches. The connectionist architecture with the learning capability of neural network and N-version programming development of a fault-tolerant technique are implemented in the proposed fuzzy logic control system. In other words, this research involves the modeling of parameterized membership functions and the partition of fuzzy linguistic variables using neural networks trained by the unsupervised learning algorithms. Based on the self-organizing algorithm, the membership function and partition of fuzzy class are not only derived automatically, but also the preconditions of fuzzy IF-THEN rules are organized. We also provide two examples, pattern recognition and tendency prediction, to demonstrate that the proposed system has a higher computational performance and its parallel architecture supports noise-tolerant capability. This generalized scheme is very satisfactory for pattern recognition and tendency prediction problems     

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.     

Employing locality in the evolutionary generation of fuzzy rulebases

Fuzzy rule bases have proven to be an effective tool for modeling complex systems and approximating functions. The generation of a fuzzy rule base has generally been accomplished by a heuristic analysis of the relationships of the underlying system or by algorithmic rule generation from training data. Automatic rule generation has utilized clustering algorithms, proximity analysis, and evolutionary techniques to identify approximate relationships between the input and the output. In this research, two general approaches for the evolutionary generation of fuzzy rules are identified and compared: global and local rule generation. Global rule production, which is the standard method of employing evolutionary techniques in fuzzy rule base generation, considers an entire rule base as an element of population. The fitness evaluation of a rule base aggregates the performance of the model over the entire space into a single value. The local approach utilizes the limited scope of a fuzzy rule to evaluate performance in regions of the input space. The local generation of rule bases employs an independent evolutionary search in each region and combines the local results to produce a global model. An experimental suite has been developed to compare the effectiveness of the two strategies for the evolutionary generation of fuzzy models.     

A fuzzy clustering-based rapid prototyping for fuzzy rule-basedmodeling

This paper presents different approaches to the problem of fuzzy rules extraction by using fuzzy clustering as the main tool. Within these approaches we describe six methods that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms. These approaches attempt to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data. Because the main objective is to obtain an approximation, the methods we propose must be as simple as possible, but also, they must have a great approximative capacity and in that way we work directly with fuzzy sets induced in the variables input space. The methods are applied to four examples and the errors obtained are specified in the different cases     

A fuzzy neural network with fuzzy impact grades

Fuzzy rule derivation is often difficult and time-consuming, and requires expert knowledge. This creates a common bottleneck in fuzzy system design. In order to solve this problem, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a fuzzy neural network based on mutual subsethood (MSBFNN) and its fuzzy rule identification algorithms. In our approach, fuzzy rules are described by different fuzzy sets. For each fuzzy set representing a fuzzy rule, the universe of discourse is defined as the summation of weighted membership grades of input linguistic terms that associate with the given fuzzy rule. In this manner, MSBFNN fully considers the contribution of input variables to the joint firing strength of fuzzy rules. Afterwards, the proposed fuzzy neural network quantifies the impacts of fuzzy rules on the consequent parts by fuzzy connections based on mutual subsethood. Furthermore, to enhance the knowledge representation and interpretation of the rules, a linear transformation from consequent parts to output is incorporated into MSBFNN so that higher accuracy can be achieved. In the parameter identification phase, the backpropagation algorithm is employed, and proper linear transformation is also determined dynamically. To demonstrate the capability of the MSBFNN, simulations in different areas including classification, regression and time series prediction are conducted. The proposed MSBFNN shows encouraging performance when benchmarked against other models.     

Multilayer fuzzy control of multivariable systems by active decomposition

The article considers the application of multilayer control theory in multivariable fuzzy systems. Some definitions and theorems with regard to such systems are given. Multilayer control algorithms, based on active decomposition of the original system into layers, are presented and illustrated by numerical examples. The algorithms use sets of transforming fuzzy relations, leading to a unilayer solution when added to the original fuzzy relations. The solution is dependent on a subset of state variables as the other variables are taken into account implicitly. It is shown that the number of measured variables and fuzzy relations is significantly reduced and thus real-time measurement and control implementation is faciliated. © 1997 John Wiley & Sons, Inc.     

A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi–Sugeno–Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.      

Neural networks that learn from fuzzy if-then rules

An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived. The learning algorithms can be viewed as an extension of the backpropagation algorithm to the case of fuzzy input vectors and fuzzy target outputs. Using the proposed methods, linguistic knowledge from human experts represented by fuzzy if-then rules and numerical data from measuring instruments can be integrated into a single information processing system (classification system or fuzzy control system). It is shown that the scheme works well for simple examples     

Approximated fuzzy logic controlled shunt active power filter for improved power quality

Shunt active power filters have been widely used for power quality improvement. With the advancement in artificial intelligence techniques, the applications of fuzzy logic‐based control systems have increased manifolds. This paper proposes a reduced rule fuzzy logic controller (FLC) in the voltage control loop of a shunt active power filter (APF), which is approximating a conventional large rule FLC. The difference between the controlled outputs of two controllers is compensated by proposed compensating factors. The dynamic response and harmonic compensation performance of proposed 4‐rule approximated fuzzy logic controller (AFLC) is compared with 25‐rule FLC. A three‐phase shunt APF is used for harmonic and reactive power compensation. The proposed scheme is tested with randomly varying single and multiple non‐linear loads. The simulation results presented under transient and steady‐state conditions confirm that the proposed 4‐rule AFLC efficiently approximates the 25‐rule FLC. The proposed control methodology takes less computational time and computational memory as the numbers of rules are reduced significantly.     

A type-2 fuzzy logic controller design for buck and boost DC–DC converters

Conventional (type-1) fuzzy logic controllers have been commonly used in various power converter applications. Generally, in these controllers, the experience and knowledge of human experts are needed to decide parameters associated with the rule base and membership functions. The rule base and the membership function parameters may often mean different things to different experts. This may cause rule uncertainty problems. Consequently, the performance of the controlled system, which is controlled with type-1 fuzzy logic controller, is undesirably affected. In this study, a type-2 fuzzy logic controller is proposed for the control of buck and boost DC–DC converters. To examine and analysis the effects of the proposed controller on the system performance, both converters are also controlled using the PI controller and conventional fuzzy logic controller. The settling time, the overshoot, the steady state error and the transient response of the converters under the load and input voltage changes are used as the performance criteria for the evaluation of the controller performance. Simulation results show that buck and boost converters controlled by type-2 fuzzy logic controller have better performance than the buck and boost converters controlled by type-1 fuzzy logic controller and PI controller.     

A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers

The paper presents a multi-objective genetic approach to design interpretability-oriented fuzzy rule-based classifiers from data. The proposed approach allows us to obtain systems with various levels of compromise between their accuracy and interpretability. During the learning process, parameters of the membership functions, as well as the structure of the classifier's fuzzy rule base (i.e., the number of rules, the number of rule antecedents, etc.) evolve simultaneously using a Pittsburgh-type genetic approach. Since there is no particular coding of fuzzy rule structures in a chromosome (it reduces computational complexity of the algorithm), original crossover and mutation operators, as well as chromosome-repairing technique to directly transform the rules are also proposed. To evaluate both the accuracy and interpretability of the system, two measures are used. The first one – an accuracy measure – is based on the root mean square error of the system's response. The second one – an interpretability measure – is based on the arithmetic mean of three components: (a) the average length of rules (the average number of antecedents used in the rules), (b) the number of active fuzzy sets and (c) the number of active inputs of the system (an active fuzzy set or input means a set or input used by at least one fuzzy rule). Both measures are used as objectives in multi-objective (2-objective in our case) genetic optimization approaches such as well-known SPEA2 and NSGA-II algorithms. Moreover, for the purpose of comparison with several alternative approaches, the experiments are carried out both considering the so-called strong fuzzy partitions (SFPs) of attribute domains and without them. SFPs provide more semantically meaningful solutions, usually at the expense of their accuracy. The operation of the proposed technique in various classification problems is tested with the use of 20 benchmark data sets and compared to 11 alternative classification techniques. The experiments show that the proposed approach generates classifiers of significantly improved interpretability, while still characterized by competitive accuracy.     

基于遗传算法获取模糊规则

针对传统利用遗传算法(GA)直接获得的模糊规则所具有的局限性问题,提出了一种带有加权因子的模糊控制规则计算方法,并利用遗传算法对加权因子进行全局寻优,最终由最优加权因子计算生成模糊规则。该计算方法针对不同的模糊输入等级施加不同的加权因子,并能够利用加权因子的相关性与对称性完整地评估所有的模糊规则,减少无效规则对系统响应所造成的影响。性能对比实验表明,该模糊规则所构成的模糊控制系统在控制过程中超调量小,调节时间短,在模糊控制的应用中具有可行性;不同激励的仿真实验表明,该模糊规则所构成的模糊控制系统的控制效果不依赖于系统的激励信号,跟踪效果好,具有很强的鲁棒性。     

Comparison of different strategies of utilizing fuzzy clustering in structure identification

Fuzzy systems approximate highly nonlinear systems by means of fuzzy “if-then” rules. In the literature, various algorithms are proposed for mining. These algorithms commonly utilize fuzzy clustering in structure identification. Basically, there are three different approaches in which one can utilize fuzzy clustering; the first one is based on input space clustering, the second one considers clustering realized in the output space, while the third one is concerned with clustering realized in the combined input-output space. In this study, we analyze these three approaches. We discuss each of the algorithms in great detail and offer a thorough comparative analysis. Finally, we compare the performances of these algorithms in a medical diagnosis classification problem, namely Aachen Aphasia Test. The experiment and the results provide a valuable insight about the merits and the shortcomings of these three clustering approaches.     

Self-organized fuzzy system generation from training examples

In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. The paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neuro-fuzzy systems, and genetic algorithms     

Genetic algorithm-based optimal fuzzy controller design in the linguistic space

In this paper, a genetic algorithm (GA) based optimal fuzzy controller design is proposed. The design procedure is accomplished by establishing an index function as the consequent part of the fuzzy control rule. The inputs of the controller, after scaling, are utilized by the index function for computing the output linguistic value. This linguistic value can then be used to map the suitable fuzzy control actions. This proposed novel fuzzy control rule has crisp input and fuzzified output characteristics. The index function plays a role in mapping the desired fuzzy sets for defuzzification resulting in a controlled hypersurface in the linguistic space formed by the input fuzzy variables. Two types of index functions, both linear and nonlinear, are introduced for controlling systems with different degrees of nonlinearity. The parameters of the index function are obtained by applying a simple GA with a suitable fitness function. Various controlled systems result in various parameter sets depending on their dynamics. Under the acquired optimal parameter set the optimal index function can be used to generate the desired control actions. Several simulation examples are given to verify the performance of the proposed GA-based fuzzy controller.     

An investigation into the application of neural networks,fuzzy logic,genetic algorithms,and rough sets to automated knowledge acquisition for classification problems

This paper presents some highlights in the application of neural networks, fuzzy logic, genetic algorithms, and rough sets to automated knowledge acquisition. These techniques are capable of dealing with inexact and imprecise problem domains and have been demonstrated to be useful in the solution of classification problems. It addresses the issue of the application of appropriate evaluation criteria such as rule base accuracy and comprehensibility for new knowledge acquisition techniques. An empirical study is then described in which three approaches to knowledge acquisition are investigated. The first approach combines neural networks and fuzzy logic, the second, genetic algorithms and fuzzy logic, and in the third a rough sets approach has been examined, and compared. In this study neural network and genetic algorithm fuzzy rule induction systems have been developed and applied to three classification problems. Rule induction software based on rough sets theory was also used to generate and test rule bases for the same data. A comparison of these approaches with the C4.5 inductive algorithm was also carried out. Our research to date indicates that, based on the evaluation criteria used, the genetic/fuzzy approach compares more than favourably with the neuro/fuzzy and rough set approaches. On the data sets used the genetic algorithm system displays a higher accuracy of classification and rule base comprehensibility than the C4.5 inductive algorithm.     

固定区间Kalman平滑新算法

用现代时间序列分析方法,基于ＡＲＭＡ新息模型和白噪声估值器,提出了一种正向固定区间稳态Ｋａｌｍａｎ平滑新算法和两种反向固定区间稳态Ｋａｌｍａｎ平滑新算法,并给出了保证算法最优性的最优初值公式。算法简单,便于实时应用。仿真例子说明了它们的有效性。