This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational power, etc., can be applied to both models directly. It is of interest to observe that twomodels stemming from different origins turn out to be functional equivalent.

Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (Adaptive-Network-based Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed.

This paper presents a generalized control strategy that enhances fuzzy controllers with selflearning capability for achieving prescribed control objectives in a near-optimal manner. This methodology, termed temporal back propagation, is model-insensitive 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, fuzzy models, etc. Regardless of the numbers of inputs and outputs of the plants under consideration, the proposed approach can either refine the fuzzy if-then rules obtained from 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. 1 Introduction Fuzzy controllers (FC's) have recently found various applications in industry as well as in household appliances. For com...

. One of the most significant cost factors in robotics applications is the design and development of real-time robot control software. Control theory helps when linear controllers have to be developed, but it doesn't sufficiently support the generation of non-linear controllers, although in many cases (such as in compliance control), nonlinear control is essential for achieving high performance. This paper discusses how Machine Learning has been applied to the design of (non-)linear controllers. Several alternative function approximators, including Multilayer Perceptrons (MLP), Radial Basis Function Networks (RBFNs), and Fuzzy Controllers are analyzed and compared, leading to the definition of two major families: Open Field Function Function Approximators and Locally Receptive Field Function Approximators. It is shown that RBFNs and Fuzzy Controllers bear strong similarities, and that both have a symbolic interpretation. This characteristics allows for applying both symbolic and statis...

We propose a neuro--fuzzy architecture for function approximation based on supervised learning. The learning algorithm is able to determine the structure and the parameters of a fuzzy system. The approach is an extension to our already published NEFCON and NEFCLASS models which are used for control or classification purposes. The proposed extended model, which we call NEFPROX, is more general and can be used for any application based on function approximation. Keywords: neuro--fuzzy system, function approximation, structure learning, parameter learning 1 Introduction Certain fuzzy systems are universal function approximators [1, 4]. In order to identify a suitable fuzzy system for a given problem, membership functions (parameters) and a rule base (structure) must be specified. This can be done by prior knowledge, by learning, or by a combination of both. If a learning algorithm is applied that uses local information and causes local modifications in a fuzzy system, this approach is us...

This paper provides an overview on evolutionary learning methods for the automated design and optimization of fuzzy logic controllers. In a genetic tuning process an evolutionary algorithm adjusts the membership functions or scaling factors of a predefined fuzzy controller based on a performance index that specifies the desired control behavior. Genetic learning processes are concerned with the automated design of the fuzzy rule base. Their objective is to generate a set of fuzzy if-then rules that establishes the appropriate mapping from input states to control actions. We describe two applications of genetic-fuzzy systems in detail, an evolution strategy that tunes the scaling and membership functions of a fuzzy cart-pole balancing controller and a genetic algorithm that learns the fuzzy control rules for an obstacle avoidance behavior of a mobile robot.

Nowadays, Fuzzy Rule-Based Systems are successfully applied to many different real-world problems. Unfortunatelly, relatively few well-structured methodologies exist for designing them and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the form of fuzzy rules. TSK Fuzzy Rule-Based Systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a two-stage evolutionary process for designing TSK Fuzzy Rule-Based Systems from examples combining a generation stage based on a (¯; )-Evolution Strategy, in which the fuzzy rules with different consequents compete among themselves to form part of a preliminary Knowledge Base, and a refinement stage, in which both the antecedent and consequent parts of the fuzzy rules in this previous Knowledge Base are adapted by a hybrid evolutionary process composed of a Genetic Algorithm and an Evolution Strategy to obtain the ...

This paper presents an innovative approach to the structure determination problem in fuzzy modeling. By using the well-known CART (classification and regression tree) algorithm as a quick preprocess, the proposed method can roughly estimate the structure (numbers of membership functions and number of fuzzy rules, etc.) of a fuzzy inference system; then the parameter identification is carried out by the hybrid learning scheme developed in our previous work [3, 2, 5]. Morevoer, the identified fuzzy inference system has the property that the total of firing strengths is always equal to one; this speeds up learning processes and reduces round-off errors. 1 Introduction Fuzzy modeling [11, 10] is a new branch of system identification which concerns with the construction of a fuzzy inference system (or fuzzy model) that can predict and hopefully explain the behavior of an unknown system described by a set of sample data. Two primary tasks of fuzzy modeling are structure determination...

As control system tasks become more demanding, more robust controller design methodologies are needed. A Genetic Algorithm (GA) optimizer, which utilizes natural evolution strategies, offers a promising technology that supports optimization of the parameters of fuzzy logic and other parameterized non-linear controllers. This paper shows how GAs can effectively and efficiently optimize the performance of fuzzy net controllers employing high performance simulation to reduce the design cycle time from hours to minutes. Our results demonstrate the robustness of a GA-based Computer-Aided System Design methodology for rapid prototyping of control systems. Keywords: Genetic Algorithms; Fuzzy Logic Control; Oxygen Production System; Inverted Pendulum. Introduction Computer-Aided System Design (CASD) should support designing various functions of high autonomy systems[10], such as normal operation control, fault-tolerance, communication, planning and scheduling. Since conventional control schem...

Functionality-based object recognition systems recognize objects at the category level by reasoning about how well the objects support the expected function of the category. Such systems naturally associate a "measure of goodness" or "membership value" with a recognized object. This measure of goodness is the result of combining individual measures, or membership values, from potentially many primitive evaluations of different properties of the object's shape. A membership function is used to compute the membership value for a primitive evaluation of a particular physical property of an object. In previous versions of a recognition system known as GRUFF, the membership function for each of the primitive evaluations had to be hand-crafted by the system designer. In this paper, we provide a learning component for the GRUFF system, called Omlet, that automatically learns primitive evaluation membership functions given a set of example objects labeled with their desired category measure. T...