Showing papers on "Fuzzy logic published in 1998"

Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs

Abstract: This paper presents new relaxed stability conditions and LMI- (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented by Takagi-Sugeno's (TS) fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the TS fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers, LMI-based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. Other LMI's with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI-based design procedures.

Learning from Data: Concepts, Theory, and Methods

Abstract: From the Publisher: This is an interdisciplinary book on neural networks, statistics and fuzzy systems. A unique feature is the establishment of a general framework for adaptive data modeling within which various methods from statistics, neural networks and fuzzy logic are presented. Chapter summaries, examples and case studies are also included.[Includes companion Web site with ... Software for use with the book.

Fuzzy Modeling for Control

Abstract: From the Publisher: Fuzzy Modeling for Control addresses fuzzy modeling from the systems and control engineering point of view. It focuses on the selection of appropriate model structures, on the acquisition of dynamic fuzzy models from process measurements (fuzzy identification), and on the design of nonlinear controllers based on fuzzy models. The main features of the presented techniques are illustrated by means of simple examples. In addition, three real-world applications are described. Finally, software tools for building fuzzy models from measurements are available from the author.

Fuzzy Logic: Intelligence, Control, and Information

Abstract: 1. Introduction. 2. Basic Concepts of Fuzzy Logic. 3. Fuzzy Sets. 4. Fuzzy Relations, Fuzzy Graphs, and Fuzzy Arithmetic. 5. Fuzzy If-Then Rules. 6. Fuzzy Implications and Approximate Reasoning. 7. Fuzzy Logic and Probability Theory. 8. Fuzzy Logic in Control Engineering. 9. Hierarchical Intelligent Control. 10. Analytical Issues in Fuzzy Logic Control. 11. Fuzzy Logic and Artificial Intelligence. 12. Fuzzy Logic in Database Management and Information Systems. 13. Fuzzy Logic in Pattern Recognition. 14. Fuzzy Model Identification. 15.Advanced Topics of Fuzzy Model Identification. 16.Neuro-Fuzzy Systems. 17. Genetic Algorithms and Fuzzy Logic. References. Index.

Fuzzy decision trees: issues and methods

Abstract: Decision trees are one of the most popular choices for learning and reasoning from feature-based examples. They have undergone a number of alterations to deal with language and measurement uncertainties. We present another modification, aimed at combining symbolic decision trees with approximate reasoning offered by fuzzy representation. The intent is to exploit complementary advantages of both: popularity in applications to learning from examples, high knowledge comprehensibility of decision trees, and the ability to deal with inexact and uncertain information of fuzzy representation. The merger utilizes existing methodologies in both areas to full advantage, but is by no means trivial. In particular, knowledge inferences must be newly defined for the fuzzy tree. We propose a number of alternatives, based on rule-based systems and fuzzy control. We also explore capabilities that the new framework provides. The resulting learning method is most suitable for stationary problems, with both numerical and symbolic features, when the goal is both high knowledge comprehensibility and gradually changing output. We describe the methodology and provide simple illustrations.

Analysis and design of fuzzy controller and fuzzy observer

Abstract: This paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of the separation property; that is, the fuzzy controller and the fuzzy observer can be independently designed. A numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer.

Introduction to type-2 fuzzy logic systems

Abstract: This paper introduces a robust fuzzy logic system, one that can handle rule uncertainties. We make use of type-2 fuzzy sets for this purpose. The development of a type-2 fuzzy logic system has led to a new operation that we call type-reduction. In the course of this development, we also study set operations on type-2 sets, properties of membership grades of type-2 sets, type-2 relations and their compositions, and defuzzification.

Mining fuzzy association rules in databases

Abstract: Data mining is the discovery of previously unknown, potentially useful and hidden knowledge in databases. In this paper, we concentrate on the discovery of association rules. Many algorithms have been proposed to find association rules in databases with binary attributes. We introduce the fuzzy association rules of the form, 'If X is A then Y is B', to deal with quantitative attributes. X, Y are set of attributes and A, B are fuzzy sets which describe X and Y respectively. Using the fuzzy set concept, the discovered rules are more understandable to human. Moreover, fuzzy sets handle numerical values better than existing methods because fuzzy sets soften the effect of sharp boundaries.

Stability analysis and design of fuzzy control systems

Abstract: The stability of a fuzzy feedback control system consisting of a fuzzy controller connected in series with a plant described by a fuzzy model is discussed. The stability analysis is based on some new theorems that guarantee sufficient conditions for asymptotical stability of the equilibrium point and total stability of the system. The stability analysis results are used to provide an approach to fuzzy controller design. The steps of the approach are specified through a design example.

A fuzzy vessel tracking algorithm for retinal images based on fuzzy clustering

Abstract: In this paper the authors present a new unsupervised fuzzy algorithm for vessel tracking that is applied to the detection of the ocular fundus vessels. The proposed method overcomes the problems of initialization and vessel profile modeling that are encountered in the literature and automatically tracks fundus vessels using linguistic descriptions like "vessel" and "nonvessel." The main tool for determining vessel and nonvessel regions along a vessel profile is the fuzzy C-means clustering algorithm that is fed with properly preprocessed data, Additional procedures for checking the validity of the detected vessels and handling junctions and forks are also presented. The application of the proposed algorithm to fundus images and simulated vessels resulted in very good overall performance and consistent estimation of vessel parameters.

Fuzzy inference system learning by reinforcement methods

Abstract: Fuzzy Actor-Critic Learning (FACL) and Fuzzy Q-Learning (FQL) are reinforcement learning methods based on dynamic programming (DP) principles. In the paper, they are used to tune online the conclusion part of fuzzy inference systems (FIS). The only information available for learning is the system feedback, which describes in terms of reward and punishment the task the fuzzy agent has to realize. At each time step, the agent receives a reinforcement signal according to the last action it has performed in the previous state. The problem involves optimizing not only the direct reinforcement, but also the total amount of reinforcements the agent can receive in the future. To illustrate the use of these two learning methods, we first applied them to a problem that involves finding a fuzzy controller to drive a boat from one bank to another, across a river with a strong nonlinear current. Then, we used the well known Cart-Pole Balancing and Mountain-Car problems to be able to compare our methods to other reinforcement learning methods and focus on important characteristic aspects of FACL and FQL. We found that the genericity of our methods allows us to learn every kind of reinforcement learning problem (continuous states, discrete/continuous actions, various type of reinforcement functions). The experimental studies also show the superiority of these methods with respect to the other related methods we can find in the literature.

A unified approach to controlling chaos via an LMI-based fuzzy control system design

Abstract: This paper presents a unified approach to controlling chaos via a fuzzy control system design based on linear matrix inequalities (LMI's). First, Takagi-Sugeno fuzzy models and some stability results are recalled. To design fuzzy controllers, chaotic systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to determine structures of fuzzy controllers from the Takagi-Sugeno fuzzy models, LMI-based design problems are defined and employed to find feedback gains of fuzzy controllers satisfying stability, decay rate, and constraints on control input and output of fuzzy control systems. Stabilization, synchronization, and chaotic model following control for chaotic systems are realized via the unified approach based on LMIs. An exact linearization (EL) technique is presented as a main result in the stabilization. The EL technique also plays an important role in the synchronization and the chaotic model following control. Two cases are considered in the synchronization. One is the feasible case of the EL problem. The other is the infeasible case of the EL problem. Furthermore, the chaotic model following control problem, which is more difficult than the synchronization problem, is discussed using the EL technique. Simulation results show the utility of the unified design approach based on LMIs proposed in this paper.

Adaptive fuzzy sliding mode control of nonlinear system

Abstract: In this paper, the fuzzy approximator and sliding mode control (SMC) scheme are considered. We propose two methods of adaptive SMC schemes that the fuzzy logic systems (approximators) are used to approximate the unknown system functions in designing the SMC of nonlinear system. In the first method, a fuzzy logic system is utilized to approximate the unknown function f of the nonlinear system x/sup n=/f(x, t)+b(x, t)u and the robust adaptive law is proposed to reduce the approximation errors between the true nonlinear functions and fuzzy approximators. In the second method, two fuzzy logic systems are utilized to approximate the f and b, respectively, and the control law, which is robust to approximation error is also designed. The stabilities of proposed control schemes are proved and these schemes are applied to an inverted pendulum system. The comparisons between the proposed control schemes are shown in simulations.

Improving the interpretability of TSK fuzzy models by combining global learning and local learning

Abstract: The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example.

Development of a systematic methodology of fuzzy logic modeling

Abstract: This paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling. It has a unified parameterized reasoning formulation, an improved fuzzy clustering algorithm, and an efficient strategy of selecting significant system inputs and their membership functions. The reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation. As a result, we are no longer restricted to standard extremes in any step of reasoning. The fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input-output data. The fuzzy rules are generated through fuzzy c-means (FCM) clustering. Major bottlenecks are addressed and analytical solutions are suggested. We also address the classification process to extend the derived fuzzy partition to the entire output space. In order to select suitable input variables among a finite number of candidates (unlike traditional approaches) we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required. Furthermore, a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions. In order to evaluate the proposed methodology, two examples-a nonlinear function and a gas furnace dynamic procedure-are investigated in detail. The significant improvement of the model is concluded compared to other fuzzy modeling approaches.

Modelling and simulation of a supply chain in an uncertain environment

Abstract: This paper describes fuzzy modelling and simulation of a supply chain (SC) in an uncertain environment, as the first step in developing a decision support system. An SC is viewed as a series of facilities that performs the procurement of raw material, its transformation to intermediate and end-products, and distribution and selling of the end-products to customers. All the facilities in the SC are coupled and interrelated in a way that decisions made at one facility affect the performance of others. SC fuzzy models and a simulator cover operational SC control. The objective is to determine the stock levels and order quantities for each inventory in an SC during a finite time horizon to obtain an acceptable delivery performance at a reasonable total cost for the whole SC. Two sources of uncertainty inherent in the external environment in which the SC operates were identified and modelled: customer demand and external supply of raw material. They were interpreted and represented by fuzzy sets. In addition to the fuzzy SC models, a special SC simulator was developed. The SC simulator provides a dynamic view of the SC and assesses the impact of decisions recommended by the SC fuzzy models on SC performance.

Combinatorial rule explosion eliminated by a fuzzy rule configuration

Abstract: Conventional fuzzy inference methodology relates the relevant subsets of each input universal set to the subsets of the other system inputs through an intersection-rule configuration. This strategy yields an exponential growth in the number of rules as inputs are added to the system, quickly reducing performance to unacceptable levels. A novel rule configuration and matrix design are presented in this paper that do not rely on rule multiplication to insure that antecedent elements are effectively related to their consequent counterparts. This alternative formulation models the entire system problem space with a simplified structure that increases linearly as the inference engine grows, providing significant computational savings to a broad range of commercial and scientific applications.

A new correlation-based fuzzy logic clustering algorithm for fMRI

Abstract: Fuzzy logic clustering algorithms are a new class of processing strategies for functional MRI (fMRI). In this study, the ability of such methods to detect brain activation on application of a stimulus task is demonstrated. An optimization of the selected algorithm with regard to different parameters is proposed. These parameters include (a) those defining the pre-processing procedure of the data set; (b) the definition of the distance between two time courses, considered as p-dimensional vectors, where p is the number of sequential images in the fMRI data set; and (c) the number of clusters to be considered. Based on the assumption that such a clustering algorithm should cluster the pixel time courses according to their similarity and not their proximity (in terms of distance), cross-correlation-based distances are defined. A clear mathematical description of the algorithm is proposed, and its convergence is proven when similarity measures are used instead of conventional Euclidean distance. The differences between the membership function given by the algorithm and the probability are clearly exposed. The algorithm was tested on artificial data sets, as well as on data sets from six volunteers undergoing stimulation of the primary visual cortex. The fMRI maps provided by the fuzzy logic algorithm are compared to those achieved by the well established cross-correlation technique.

Decoupled fuzzy sliding-mode control

Abstract: A decoupled fuzzy sliding-mode controller design is proposed. The decoupled method provides a simple way to achieve asymptotic stability for a class of fourth-order nonlinear systems with only five fuzzy control rules. The ideas behind the controller are as follows. First, decouple the whole system into two second-order systems such that each subsystem has a separate control target expressed in terms of a sliding surface. Then, information from the secondary target conditions the main target, which, in turn, generates a control action to make both subsystems move toward their sliding surface, respectively. A closely related fuzzy controller to the sliding-mode controller is also presented to show the theoretical aspect of the fuzzy approach in which the characteristics of fuzzy sets are determined analytically to ensure the stability and robustness of the fuzzy controller. Finally, the decoupled sliding-mode control (SMC) is used to control three highly nonlinear systems and confirms the validity of the proposed approach.

On fuzzy logic applications for automatic control, supervision, and fault diagnosis

Abstract: The degree of vagueness of variables, process description, and automation functions is considered and is shown. Where quantitative and qualitative knowledge is available for design and information processing within automation systems. Fuzzy-rule-based systems with several levels of rules form the basis for different automation functions. Fuzzy control can be used in many ways, for normal and for special operating conditions. Experience with the design of fuzzy controllers in the basic level is summarized, as well as criteria for efficient applications. Different fuzzy control schemes are considered, including cascade, feedforward, variable structure, self-tuning, adaptive and quality control leading to hybrid classical/fuzzy control systems. It is then shown how fuzzy logic approaches can be applied to process supervision and to fault diagnosis with approximate reasoning on observed symptoms. Based on the properties of fuzzy logic approaches the contribution gives a review and classification of the potentials of fuzzy logic in process automation.