Fuzzy logic controller design for spacecraft proximity operations

A Genetic Algorithms (GAs) based method is presented in this paper for concurrent design of rule sets and membership functions for a fuzzy logic controllers to be used in spacecraft proximity operations. The heuristic nature of fuzzy logic makes GAs a natural candidate for logic design in which both rule sets and membership functions are optimized simultaneously. The employment of GAs natural genetic operations provides a means to search in a complex system space that is difficult to described mathematically. A one-dimensional controller for spacecraft proximity operations is implemented for examination in detail. The expension of the algorithm for a 6 DOP controller is discussed.     

Design of adaptive fuzzy logic controller based on linguistic-hedgeconcepts and genetic algorithms

In this paper, we propose a novel fuzzy logic controller, called linguistic hedge fuzzy logic controller, to simplify the membership function constructions and the rule developments. The design methodology of linguistic hedge fuzzy logic controller is a hybrid model based on the concepts of the linguistic hedges and the genetic algorithms. The linguistic hedge operators are used to adjust the shape of the system membership functions dynamically, and ran speed up the control result to fit the system demand. The genetic algorithms are adopted to search the optimal linguistic hedge combination in the linguistic hedge module, According to the proposed methodology, the linguistic hedge fuzzy logic controller has the following advantages: 1) it needs only the simple-shape membership functions rather than the carefully designed ones for characterizing the related variables; 2) it is sufficient to adopt a fewer number of rules for inference; 3) the rules are developed intuitionally without heavily depending on the endeavor of experts; 4) the linguistic hedge module associated with the genetic algorithm enables it to be adaptive; 5) it performs better than the conventional fuzzy logic controllers do; and 6) it can be realized with low design complexity and small hardware overhead. Furthermore, the proposed approach has been applied to design three well-known nonlinear systems. The simulation and experimental results demonstrate the effectiveness of this design.     

Simplifying the automatic design of a fuzzy logic controller using evolutionary programming

With the availability of a wide range of Evolutionary Algorithms such as Genetic Algorithms, Evolutionary Programming, Evolutionary Strategies and Differential Evolution, every conceivable aspect of the design of a fuzzy logic controller has been optimized and automated. Although there is no doubt that these automated techniques can produce an optimal fuzzy logic controller, the structure of such a controller is often obscure and in many cases these optimizations are simply not needed. We believe that the automatic design of a fuzzy logic controller can be simplified by using a generic rule base such as the MacVicar-Whelan rule base and using an evolutionary algorithm to optimize only the membership functions of the fuzzy sets. Furthermore, by restricting the overlapping of fuzzy sets, using triangular membership functions and singletons, and reducing the number of parameters to represent the membership functions, the design can be further simplified. This paper describes this method of simplifying the design and some experiments performed to ascertain its validity.     

Complex fuzzy logic

A novel framework for logical reasoning, termed complex fuzzy logic, is presented in this paper. Complex fuzzy logic is a generalization of traditional fuzzy logic, based on complex fuzzy sets. In complex fuzzy logic, inference rules are constructed and "fired" in a manner that closely parallels traditional fuzzy logic. The novelty of complex fuzzy logic is that the sets used in the reasoning process are complex fuzzy sets, characterized by complex-valued membership functions. The range of these membership functions is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane, thus providing a method for describing membership in a set in terms of a complex number. Several mathematical properties of complex fuzzy sets, which serve as a basis for the derivation of complex fuzzy logic, are reviewed in this paper. These properties include basic set theoretic operations on complex fuzzy sets - namely complex fuzzy union and intersection, complex fuzzy relations and their composition, and a novel form of set aggregation - vector aggregation. Complex fuzzy logic is designed to maintain the advantages of traditional fuzzy logic, while benefiting from the properties of complex numbers and complex fuzzy sets. The introduction of complex-valued grades of membership to the realm of fuzzy logic generates a framework with unique mathematical properties, and considerable potential for further research and application.     

Adaptive fuzzy PI controller with shifted control singletons

It is well known the fact that the design of a fuzzy control system is based on the human expert experience and control engineer knowledge regarding the controlled plant behavior. As a direct consequence, a fuzzy control system can be considered as belonging to the class of intelligent expert systems. The tuning procedure of a fuzzy controller represents a quite difficult and meticulous task, being based on prior data regarding good knowledge of the controlled plant. The complexity of the tuning procedure increases with the number of the fuzzy linguistic variables and, consequently, of the fuzzy inference rules and thus, the tuning process becomes more difficult. The paper presents a new design strategy for such expert fuzzy system, which improves their performance without increasing the number of fuzzy linguistic variables. The novelty consists in extending the classic structure of the fuzzy inference core with an intelligent module, which tunes one of the control singletons, providing a significant simplification of the design and implementation procedure. The proposed strategy implements a logical, not physical, supplementation of the linguistic terms associated to the controller output. Therefore, a fuzzy rules set with a reduced number of linguistic terms is used to implement the expert control system. This logical supplementation is based on an intelligent algorithm which performs a shifting of only one of the control singletons (the singleton associated to the SMALL_ linguistic variable), its value becoming variable, a fact that allows an accurate control and a better performance for the expert control system. The logic of this intelligent algorithm is to initially provide a high controller output, followed by a slowdown of the control signal near to the operating set point. The main advantage of the proposed expert control strategy is its simplicity: a reduced number of linguistic terms, combined with an intelligent tuning of a single parameter, can provide results as accurate as other more complex available solutions involving tuning of several parameters (well described by the technical literature). Also, a simplification of the preliminary off-line tuning procedure is performed by using a reduced set of fuzzy rules. The generality of the proposed expert control strategy allows its use for any other controlled process.     

语言标记Vague集及其应用

为了解决不确定环境有时不能提供给Vague集的真、假隶属度以精确数字值的问题, 文中提出了语言标记Vague(Linguistic Label Vague,LLV)集.其论域对象的真、假隶属度均是 意义为模糊集的语言标记.文中还定义了LLV集的补、并、交和包含运算.作为应用,构造了LLV 决策表;获取了LLV决策规则;通过LLV集包含程度和相交程度度量了规则的强度,用LLV值 记分函数对强度排序.仿真结果表明:LLV集有时比Vague集更为现实地表示不精确信息.     

Analytical structure and stability analysis of a fuzzy PID controller

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum inference method, and center of sums (COS) defuzzification method. Conditions for bounded-input bounded-output (BIBO) stability are derived using the Small Gain Theorem. Finally, two numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controller.     

Circuit implementation of linguistic-hedge fuzzy logic controller in current-mode approach

In this paper, a novel fuzzy logic controller called linguistic-hedge fuzzy logic controller in a mixed-signal circuit design is discussed. The linguistic-hedge fuzzy logic controller has the following advantages: 1) it needs only three simple-shape membership functions for characterizing each variable prior to the linguistic-hedge modifications; 2) it is sufficient to adopt nine rules for inference; 3) the rules are developed intuitively without heavy dependence on the endeavors of experts; 4) it performs better than conventional fuzzy logic controllers; and 5) it can be realized with a lower design complexity and a smaller hardware overhead as compared with the controllers that required more than nine rules. In this implementation, a current-mode approach is adopted in designing the signal processing portions to simplify the circuit complexity; digital circuits are adopted to implement the programmable units. This design was fabricated with a TSMC 0.35 /spl mu/m single-polysilicon-quadruple-metal CMOS process. In this chip, the LHFLC processes two input variables and one output variable. Each variable is specified using three membership functions. Nine inference rules, scheduled in a rule table with a dimension of 3 /spl times/ 3, define the relationship implications between these three variables. Under a supply voltage of 3.3 V, the measurement results show that the measured control surface and the control goal are consistent. The speed of inference operation goes up to 0.5M FLIPS that is fast enough for the control application of the cart-pole balance system. The cart-pole balance system experimental results show that this chip works with nine inference rules. Furthermore, by performing some off-chip modifications, such as shifting and scaling on the input signals and output signal of this design, according to the specifications defined by the controlled plants, this design is suitable for many control applications.     

Theoretical and linguistic aspects of the fuzzy logic controller

Successful applications of the fuzzy logic controller by various researchers to a variety of ill-defined processes motivated this theoretical study of the fuzzy logic controller. Initially the controller is analysed by traditional (nonlinear) algebraic methods which are particularly useful in stability studies, provided the process is algebraically modelled. Despite the success of this technique, it suffers from a major limitation in that the algebraic model of the controller cannot directly deal with the linguistic aspects of the fuzzy logic controller. This observation leads to the introduction of a more concise, and hence more powerful, notation for representing the linguistic rules that describe the fuzzy logic controller. The so-called linguistic models that arise from this notation are shown to be extremely useful for modelling highly nonlinear low-order systems and for determining, explicitly, the rules of ‘optimal’ fuzzy logic controllers.     

Extracting linguistic rules from data sets using fuzzy logic and genetic algorithms

Linguistic rules in natural language are useful and consistent with human way of thinking. They are very important in multi-criteria decision making due to their interpretability. In this paper, our discussions concentrate on extracting linguistic rules from data sets. In the end, we firstly analyze how to extract complex linguistic data summaries based on fuzzy logic. Then, we formalize linguistic rules based on complex linguistic data summaries, in which, the degree of confidence of linguistic rules from a data set can be explained by linguistic quantifiers and its linguistic truth from the fuzzy logical point of view. In order to obtain a linguistic rule with a higher degree of linguistic truth, a genetic algorithm is used to optimize the number and parameters of membership functions of linguistic values. Computational results show that the proposed method is an alternative method for extracting linguistic rules with linguistic truth from data sets.     

基于GA-Vague集自适应PID控制器设计

提出了一种基于GA-Vague集相似度量推理的自适应PID控制器的设计方法。该控制器由三部分组成：（1）遗传算法对模糊推理规则的优化;（2）Vague集推理规则表精确量的计算;（3）基于Vague集相似度量的自适应PID设计。该控制器弥补了模糊PID控制器的不足,模糊变量隶属值难以确定,描述信息单一,又充分发挥了遗传算法的寻优能力,对推理规则表优化,得到最佳组合的PID控制,以确保系统的响应具有最优的动态和稳态性能。仿真结果表明,控制器具有响应速度快,稳态精度高等特点,可用于控制不同的对象和过程。     

Simultaneous design of membership functions and rule sets for fuzzycontrollers using genetic algorithms

This paper examines the applicability of genetic algorithms (GA's) in the simultaneous design of membership functions and rule sets for fuzzy logic controllers. Previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions; however, the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology. When GA's have been used to develop both, it has been done serially, e.g., design the membership functions and then use them in the design of the rule set. This, however, means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently. GA's are fully capable of creating complete fuzzy controllers given the equations of motion of the system, eliminating the need for human input in the design loop. This new method has been applied to two problems, a cart controller and a truck controller. Beyond the development of these controllers, we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules     

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.     

Tuning of a neuro-fuzzy controller by genetic algorithm

Due to their powerful optimization property, genetic algorithms (GAs) are currently being investigated for the development of adaptive or self-tuning fuzzy logic control systems. This paper presents a neuro-fuzzy logic controller (NFLC) where all of its parameters can be tuned simultaneously by GA. The structure of the controller is based on the radial basis function neural network (RBF) with Gaussian membership functions. The NFLC tuned by GA can somewhat eliminate laborious design steps such as manual tuning of the membership functions and selection of the fuzzy rules. The GA implementation incorporates dynamic crossover and mutation probabilistic rates for faster convergence. A flexible position coding strategy of the NFLC parameters is also implemented to obtain near optimal solutions. The performance of the proposed controller is compared with a conventional fuzzy controller and a PID controller tuned by GA. Simulation results show that the proposed controller offers encouraging advantages and has better performance.     

一种控制机械手的自调节模糊逻辑控制器

介绍了一种机械手的模糊逻辑控制的新方法.它能根据系统的前期响应自动修改 误差变化率的隶属函数来获得理想的控制特性.在研究隶属函数对控制特性影响的基础上, 首先确定一族参数化的隶属函数.然后,用Nelder-Mead单纯形算法优化模糊逻辑控制器. 最后,用该模糊控制器控制一个具有非线性动力学特征的两自由度机械手,验证了所提方案 的有效性和鲁棒性.     

A self-learning and tuning fuzzy logic controller based on genetic algorithms and reinforcements

This article presents a new method for learning and tuning a fuzzy logic controller automatically. A reinforcement learning and a genetic algorithm are used in conjunction with a multilayer neural network model of a fuzzy logic controller, which can automatically generate the fuzzy control rules and refine the membership functions at the same time to optimize the final system's performance. In particular, the self-learning and tuning fuzzy logic controller based on genetic algorithms and reinforcement learning architecture, which is called a Stretched Genetic Reinforcement Fuzzy Logic Controller (SGRFLC), proposed here, can also learn fuzzy logic control rules even when only weak information, such as a binary target of “success” or “failure” signal, is available. We extend the AHC algorithm of Barto, Sutton, and Anderson to include the prior control knowledge of human operators. It is shown that the system can solve a fairly difficult control learning problem more concretely, the task is a cart–pole balancing system, in which a pole is hinged to a movable cart to which a continuously variable control force is applied. © 1997 John Wiley & Sons, Inc.     

Training fuzzy logic controller software components by combining adaptation algorithms

An approach for an effective and efficient off-line training of particular classes of reusable controller software components is presented. To build a necessary relationship between a component's abstract and concrete levels, each control software component is represented at the abstract level by means of a set of adaptive fuzzy logic rules and at the concrete level by means of adaptive fuzzy membership functions. Training includes two phases: testing and adapting. The testing phase is for identifying faulty fuzzy elements of a component, while the adapting phase is for modifying membership functions. We employ genetic algorithms, neural network algorithms, Monte Carlo algorithms, and their combinations in each phase. This approach is illustrated by training automotive controller software components (simulation). Experimental simulation results show that our off-line training approach supports controller software component adaptation effectively and efficiently in terms of controlled process operation accuracy and effort spent.     

用于模糊控制器设计的遗传算法研究

将遗传操作用于模糊规则和控制器参数编码，实现输入变量的合理组合、模糊规则的获取和控制器参数的优化，设计者仅需给出一个运行遗传算法(GA)的个体适应度函数。同时将模拟退火算法(SA)用于优化控制器参数，这种GASA混合优化策略在模糊控制器设计中取得了良好的效果。实例表明了算法的有效性。     

Design of a fuzzy controller in mobile robotics using genetic algorithms

The design of fuzzy controllers for the implementation of behaviors in mobile robotics is a complex and highly time-consuming task. The use of machine learning techniques, such as evolutionary algorithms or artificial neural networks for the learning of these controllers allows to automate the design process. In this paper, the automated design of a fuzzy controller using genetic algorithms for the implementation of the wall-following behavior in a mobile robot is described. The algorithm is based on the Iterative Rule Learning (IRL) approach, and a parameter (δ) is defined with the aim of selecting the relation between the number of rules and the quality and accuracy of the controller. The designer has to define the universe of discourse and the precision of each variable, and also the scoring function. No restrictions are placed neither in the number of linguistic labels nor in the values that define the membership functions.