Self-learning fuzzy controllers based on temporal backpropagation

A generalized control strategy that enhances fuzzy controllers with self-learning capability for achieving prescribed control objectives in a near-optimal manner is presented. This methodology, termed temporal backpropagation, is model-sensitive in the sense that it can deal with plants that can be represented in a piecewise-differentiable format, such as difference equations, neural networks, GMDH structures, and fuzzy models. Regardless of the numbers of inputs and outputs of the plants under consideration, the proposed approach can either refine the fuzzy if-then rules of human experts or automatically derive the fuzzy if-then rules if human experts are not available. The inverted pendulum system is employed as a testbed to demonstrate the effectiveness of the proposed control scheme and the robustness of the acquired fuzzy controller.     

基于规则插入的自适应模糊控制器的设计

提出一种为模糊控制器系统开发有效规则的自适应模糊控制器的设计方法.该方法首先基于两个基本的If-then模糊规则,然后插入多个新If_then模糊规则,其合成的模糊规则的输入_输出映射保持不变,且其隶属函数的参数在线约束为最小化成本函数,最后以最典型的非线性和延迟系统模型为例进行仿真实验,结果证明了该设计方法的有效性.     

Design and analysis of region-wise linear fuzzy controllers

In this paper, a methodology to reduce the complexity of a robust controller based on fuzzy if-then rules is proposed. The motivation and the design of this complexity-reduced fuzzy controller are presented. This fuzzy controller with the triangular membership functions and fuzzy partition methods used here leads to a region-wise linear fuzzy controller (RLFC). The properties of the region-wise linear fuzzy controllers are discussed and the reasons why they in general perform better than the PD controllers are also provided. And the simulation results based on a second order plant are included to show that the region-wise linear fuzzy controller outperforms the PD controller. We also show that the region-wise linear fuzzy controller and original fuzzy controller have similar performances.     

An approach to fuzzy default reasoning for function approximation

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions     

Performance evaluation of fuzzy classifier systems formultidimensional pattern classification problems

We examine the performance of a fuzzy genetics-based machine learning method for multidimensional pattern classification problems with continuous attributes. In our method, each fuzzy if-then rule is handled as an individual, and a fitness value is assigned to each rule. Thus, our method can be viewed as a classifier system. In this paper, we first describe fuzzy if-then rules and fuzzy reasoning for pattern classification problems. Then we explain a genetics-based machine learning method that automatically generates fuzzy if-then rules for pattern classification problems from numerical data. Because our method uses linguistic values with fixed membership functions as antecedent fuzzy sets, a linguistic interpretation of each fuzzy if-then rule is easily obtained. The fixed membership functions also lead to a simple implementation of our method as a computer program. The simplicity of implementation and the linguistic interpretation of the generated fuzzy if-then rules are the main characteristic features of our method. The performance of our method is evaluated by computer simulations on some well-known test problems. While our method involves no tuning mechanism of membership functions, it works very well in comparison with other classification methods such as nonfuzzy machine learning techniques and neural networks.     

FINDING SIMPLIFIED FUZZY IF-THEN RULES FOR FUNCTION APPROXIMATION PROBLEMS USING A FUZZY DATA MINING APPROACH

ABSTRACT

A fuzzy if-then rule whose consequent part is a real number is referred to as a simplified fuzzy rule. Since no defuzzification is required for this rule type, it has been widely used in function approximation problems. Furthermore, data mining can be used to discover useful information by exploring and analyzing data. Therefore, this paper proposes a fuzzy data mining approach to discover simplified fuzzy if-then rules from numerical data in order to approximate an unknown mapping from input to output. Since several pre-specified parameters for deriving fuzzy rules are not easily specified, they are automatically determined by the genetic algorithm with binary chromosomes. To evaluate performance of the proposed method, computer simulations are performed on various numerical data sets, showing that the fitting ability and the generalization ability of the proposed method are comparable to the known fuzzy rule-based methods.     

基于遗传算法的多维模糊分类器构造的研究

讨论了基于模糊遗传机器学习机制的密歇根方法在多维分类问题上的应用及性能问题,并提出了一种新的模糊遗传学习方法.将每一模糊规则作为遗传算法中的一个个体,且具有相应的适应度函数值.在提取模糊规则的同时,还对每个属性维的模糊划分进行学习以获取较好的模糊集合参数.另外,该方法引入了基于相似性的选择机制,减轻了选择机制对低适应函数值个体造成的选择压力,保持了种群的多样性,从而有效地避免了遗传算法收敛到局部解的问题.实验结果表明,该方法在多维模糊分类器的构造问题上具有较高的正确分类率、适应性较好等性能.     

时滞系统的模糊旋转优化控制

针对一般的模糊控制器对时滞系统难以获得精确控制的现状,提出一种经过模糊旋转优化规则方法改进后的模糊控制器设计。旋转优化分为内圈旋转优化和外圈旋转优化两部分,内圈最优化规则和外圈最优化规则组合成一个完整的模糊规则表,这个规则表最趋近于最优规则。然后将基于改进后的模糊规则建立的模糊控制器应用到纯时间滞后系统的控制中。仿真实验结果表明模糊旋转优化方法得到的模糊控制器比常规的PID控制器和Smith预估控制器的控制性能优良,并且具有超调量小,稳态时间短,鲁棒性强等优点。     

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     

A robust integrator algorithm with genetic based fuzzy controller feedback for direct vector control

The voltage model used for direct vector control has in the flux calculation process an open integration problem, which is generally solved with a feedback loop. In this paper, a new design method is developed for the feedback loop of the integrator. The method, as apart from standards in the literature, uses a fuzzy controller. Fuzzy controllers are knowledge-based systems that include fuzzy rules and fuzzy membership functions to incorporate human knowledge into their knowledge base. The determination of these rules and membership functions is one the key problems when designing fuzzy controllers, and is generally affected by subjective decisions. In this study, a fuzzy controller with rules and membership functions determined by genetic algorithms (GAs) in this study is designed and tested on various motors of different power ratings. The proposed method is simulated by using MATLAB/SIMULINK and implemented on an experimental system using a TMS320C31 digital signal processor.     

An adaptive neural fuzzy filter and its applications

A new kind of nonlinear adaptive filter, the adaptive neural fuzzy filter (ANFF), based upon a neural network's learning ability and fuzzy if-then rule structure, is proposed in this paper. The ANFF is inherently a feedforward multilayered connectionist network which can learn by itself according to numerical training data or expert knowledge represented by fuzzy if-then rules. The adaptation here includes the construction of fuzzy if-then rules (structure learning), and the tuning of the free parameters of membership functions (parameter learning). In the structure learning phase, fuzzy rules are found based on the matching of input-output clusters. In the parameter learning phase, a backpropagation-like adaptation algorithm is developed to minimize the output error. There are no hidden nodes (i.e., no membership functions and fuzzy rules) initially, and both the structure learning and parameter learning are performed concurrently as the adaptation proceeds. However, if some linguistic information about the design of the filter is available, such knowledge can be put into the ANFF to form an initial structure with hidden nodes. Two major advantages of the ANFF can thus be seen: 1) a priori knowledge can be incorporated into the ANFF which makes the fusion of numerical data and linguistic information in the filter possible; and 2) no predetermination, like the number of hidden nodes, must be given, since the ANFF can find its optimal structure and parameters automatically     

Determining optimal quality distribution of latex weight using adaptive neuro-fuzzy modeling and control systems

This paper introduces a systematic approach for the design of an adaptive neuro-fuzzy inference system (ANFIS) for latex weight control of level loop carpets. In high production volume of some industries, manual control could lead to undesirable variations in product quality. Therefore, process parameters require continuous checking and testing against quality standards. One way to overcome this problem is to use statistical process control by which a complete elimination of variability may not be possible. Fuzzy logic (FL) control is one of the most significant applications of fuzzy logic and fuzzy set theory. Fuzzy if-then rules (controllers) were developed in a systematic way that formed the backbone of the neuro-fuzzy control system. The developed ANFIS was able to produce crisp numerical outcomes to predict latex weights. The neuro-fuzzy system behaved like human operators. ANFIS outcomes were encouraging because they provide a more efficient and uniform distribution of latex weight and seemed to be better than the other statistical process control tools. FL controllers provide a feasible alternative to capture approximate, qualitative aspects of human reasoning and decision making processes.     

Selecting fuzzy if-then rules for classification problems usinggenetic algorithms

This paper proposes a genetic-algorithm-based method for selecting a small number of significant fuzzy if-then rules to construct a compact fuzzy classification system with high classification power. The rule selection problem is formulated as a combinatorial optimization problem with two objectives: to maximize the number of correctly classified patterns and to minimize the number of fuzzy if-then rules. Genetic algorithms are applied to this problem. A set of fuzzy if-then rules is coded into a string and treated as an individual in genetic algorithms. The fitness of each individual is specified by the two objectives in the combinatorial optimization problem. The performance of the proposed method for training data and test data is examined by computer simulations on the iris data of Fisher     

一个新混沌系统的自适应模糊同步

本文基于Takagi-Sugeno(T-S)模糊模型,研究了混沌系统的自适应同步。基于T-S模糊模型重构了混沌系统,推导了在衰减率α下,自适应同步全局渐近稳定的充分条件;同时,在驱动系统参数未知的情况下,使用自适应参数调节律,得到响应系统参数的估计值。设计的模糊控制器均由线性函数构成,结构简单,规则少,有利于实际应用中构造控制器。数值仿真结果验证了方法的有效性。     

Optimal PID-type fuzzy logic controller for a multi-input multi-output active magnetic bearing system

The performance of the fuzzy controllers depends highly on the proper selection of some design parameters which is usually tuned iteratively via a trial and error process based primarily on engineering intuition. With the recent developments in the area of global optimization, it has been made possible to obtain the optimal values of the design parameters systematically. Nevertheless, it is well known that unless a priori knowledge is available about the optimization search-domain, most of the available time-domain objective functions may result in undesirable solutions. It is consequently important to provide guidelines on how these parameters affect the closed-loop behavior. As a result, some alternative objective functions are presented for the time-domain optimization of the fuzzy controllers, and the design parameters of a PID-type fuzzy controller are tuned by using the proposed time-domain objective functions. Finally, the real-time application of the optimal PID-type fuzzy controller is investigated on the robust stabilization of a laboratory active magnetic bearing system. The experimental results show that the designed PID-type fuzzy controllers provide much superior performances than the linear on-board controllers while retaining lower profiles of control signals.     

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.     

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.     

Stable adaptive fuzzy control of nonlinear systems

A direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy if-then control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded is developed. The specific formula for the bounds is provided, so that controller designers can determine the bounds based on their requirements. The direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the Duffing chaotic system to track a trajectory. The simulation results show that the controller worked without using any fuzzy control rules, and that after fuzzy control rules were incorporated the adaptation speed became much faster. It is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control     

基于遗传算法的污水处理模糊控制方法

模糊控制中的模糊推理规则和隶属函数的选取往往依据相关专家或技术人员的实际经验,对具有较强的非线性系统和未知动态环境条件下,其控制性能往往达不到很好的效果.使用遗传算法同时对隶属函数和模糊规则进行优化,从而使模糊推理规则和隶属函数的确定摆脱了人为经验的局限,提高了模糊控制的自适应能力.在此基础上设计出模糊控制器,并将其应用于污水处理溶解氧的控制中.实验结果表明,该控制器能够使溶解氧快速、准确地达到期望的要求.