Takeshi Yamakawa

A fuzzy inference engine in nonlinear analog mode and its application to a fuzzy logic control

In this tutorial, the utility of a fuzzy system is demonstrated by providing a broad overview, emphasizing analog mode hardware, along with a discussion of the authors original work. First, the difference between deterministic words and fuzzy words is explained as well as fuzzy logic. The description of the system using mathematical equations, linguistic rules, or parameter distributions (e.g., neural networks) is discussed. Fuzzy inference and defuzzification algorithms are presented, and their hardware implementation is discussed. The fuzzy logic controller was used to stabilize a glass with wine balanced on a finger and a mouse moving around a plate on the tip of an inverted pendulum.

Stablization of an inverted pendulum by a high-speed fuzzy logic controller hardware system

Abstract A high-speed fuzzy controller hardware system employing Min-Max operations is presented. It has fifteen control rule boards and one defuzzifier. Grades of membership are represented with 0 V ∼ 5 V corresponding to 0.0 ∼ 1.0. This fuzzy controller facilitates approximate reasoning at 1 000 000 FIPS (fuzzy inferences per second) and is able to be used for various purposes by programming on each control rule board. It handles fuzzy linguistic information of the form NL (negative large), NM (negative medium), NS (negative small), ZR (approximately zero), PS (positive small), PM (positive medium), PL (positive large) and NG (negation). This fuzzy controller hardware system makes an inverted pendulum stand on a vehicle by using seven control rules. Two pendulums (5 mm diameter, 15 cm length, 3.5 g weight; respectively 10 mm, 50 cm, and 50 g) can be stabilized by the same rule set. It is much easier to produce control rules than to solve the nonlinear differential equations representing the dynamics of an inverted pendulum. This fuzzy controller hardware system can be applied to attitude control of a space booster rocket and satellite, an automatic aircraft landing system, pattern recognition, stabilization of nuclear fuel rods in a reactor, an intelligent sensor, and many other applications which need swift approximate reasoning.

A genetic algorithm for general machine scheduling problems

This paper deals with the so-called general machine scheduling problems. In the general machine scheduling problems, job shop type jobs and open shop type jobs are scheduled together and the imposition of precedence constraints is allowed between operations belonging to either the same job or different jobs. This paper proposes a genetic algorithm to solve such general machine scheduling problems. Some experimental results are presented to show the applicability of the proposed method. The method can be used to solve traditional job shop scheduling, flow shop scheduling, and open shop scheduling as well as general machine scheduling problems.

Silicon Implementation for a Novel High-Speed Fuzzy Inference Engine: Mega-Flips Analog Fuzzy Processor

This article describes two types of analog fuzzy processors. One is a rule chip FP-9000 and the other a defuzzifier chip FP-9001, and both can achieve high-speed fuzzy inference. The inference speed is more than 1 Mega fuzzy logical inferences per second, excluding defuzzification. The rule chip includes four fuzzy inference engines. Each engine achieves one fuzzy inference, which is characterized by a fuzzy if-then rule, in analog mode. These rules can be directly read out and written in through an external digital computer. The rule chip is fabricated in 2 μm BiCMOS technology. The defuzzifier chip converts a fuzzy value to a crisp one, necessary for a fuzzy control system. The defuzzifier chip is implemented by 3 μm bipolar technology. A high-speed fuzzy controller hardware system can be efficiently constructed with these chips. The chips accelerate to develop fuzzy logic systems, especially high-speed applications.

High-speed fuzzy controller hardware system: the Mega-FIPS machine

Abstract A high-speed fuzzy controller hardware system employing min-max operations is presented. It facilitates approximate reasoning at 1,000,000 FIPS (fuzzy inferences per second) and is able to be used for various purposes in programming. This is the first step in the approach to a fuzzy computer.

Wavelet neural networks employing over-complete number of compactly supported non-orthogonal wavelets and their applications

This paper proposes two types of new neuron models, WS neuron (wavelet synapse neuron) and WA neuron (wavelet activation function neuron), which are obtained by modifying a traditional neuron model with non-orthogonal wavelet bases, while Boubez et al. (1993) employed orthonormal wavelets. Four types of typical wavelet neural networks employing WS and/or WA neurons are discussed. The simplest wavelet neural network exhibits much higher ability of generalization and much shorter time for learning rather than a three-layered feedforward neural network. Furthermore the wavelet neural network is guaranteed to give the global minimum. Other three wavelet neural networks are examined for predicting chaotic behaviour of a nonlinear dynamical system. The performance in learning speed and prediction of wavelet neural networks are more significant than a four-layered feedforward neural network.<<ETX>>

A fuzzy logic controller

This paper describes a fuzzy sets method which is very useful for handling uncertainties and essential for knowledge acquisition of a human expert. Kinetics of a reactor is often complex and not trivial to describe by mathematical equations. Reactor control by traditional control technology is therefore difficult. A novel technology is presented. In the following a fuzzy inference (approximate reasoning) is used for decision making in analogy to human thinking, facilitating a more sophisticated control. Readers of this paper do not need any advanced mathematics beyond the four basic operations in arithmetic (+, -, x, divided by) and using the maximum and minimum values. This fuzzy inference is introduced to construct a fuzzy logic controller which is suitable for a nonlinear, multivariable and time variant system applied to a bioreactor.

FEEDBACK SELF-ORGANIZING MAP AND ITS APPLICATION TO SPATIO-TEMPORAL PATTERN CLASSIFICATION

In this paper, a feedback self-organizing map (FSOM), which is an extension of the self-organizing map (SOM) by employing feedback loops, is proposed. The SOM consists of an input layer and a competitive layer, and the input vectors applied to the input layer are mapped to the competitive layer keeping their spatial features. In order to embed the temporal information to the SOM, feedback loops from the competitive layer to the input layer are employed. The winner unit in the competitive layer is not assigned by only current input vector but also past winner units, thus the temporal information can be embedded. The effectiveness and validity of the proposed FSOM are verified by applying it to a spatio-temporal pattern classification.

A design algorithm of membership functions for a fuzzy neuron using example-based learning

The authors describe a design algorithm for extraction of membership functions of a fuzzy neuron based on example-based learning with optimization of cross-detecting lines. This algorithm facilitates design without the knowledge of experts. The algorithm was verified by recognition of hand-written characters. Using this algorithm, a fuzzy neuron can be designed very easily without knowledge about the features of the character, and optimum membership functions can be extracted.<<ETX>>

Soft Computing Based Signal Prediction, Restoration, and Filtering

In this chapter, soft computational signal processing, especially devoted to prediction, restoration and filtering of signals, is discussed. The neo-fuzzy-neuron, developed by the authors, are applied to the prediction and restoration of damaged signals. The chaotic signals and the speech signals are employed for the experiments. The filtering of noisy signals based on the Radial Basis Function (RBF) network, a special class of a fuzzy neural network, is also discussed. The proposed filter can eliminate not only Gaussian noise but also noise with an arbitrary distribution.