Ongard Sirisaengtaksin

Fuzzy control as a universal control tool

Abstract It is known that fuzzy control is a universal control tool , because an arbitrary control strategy (in particular, a control strategy that is in some sense optimal) can be obtained in principle by applying a fuzzy control methodology to some set of rules. This result has already been proved (e.g., [2, 7, 20, 21]) for the case when a plant is described by finitely many parameters and a special type of fuzzy control methodology is used. In this paper, we prove it for arbitrary plants (including plants that are distributed systems , i.e., plants whose state requires infinitely many parameters to describe) and arbitrary fuzzy control methodologies. We also prove that there exists a universal fuzzy controller that generates an appropriate control from an input description of a plant (and the desired objective). Mathematically, we prove that fuzzy systems can approximate arbitrary continuous functionals, thus generalizing a known result about continuous functions.

Wavelet neural networks are asymptotically optimal approximators for functions of one variable

Neural networks are universal approximators. For example, it has been proved (K. Hornik et al., 1989) that for every /spl epsiv/>0 an arbitrary continuous function on a compact set can be /spl epsiv/-approximated by a 3-layer neural network. This and other results prove that in principle, any function (e.g., any control) can be implemented by an appropriate neural network. But why neural networks? In addition to neural networks, an arbitrary continuous function can be also approximated by polynomials, etc. What is so special about neural networks that make them preferable approximators? To compare different approximators, one can compare the number of bits that we must store in order to be able to reconstruct a function with a given precision /spl epsiv/. For neural networks, we must store weights and thresholds. For polynomials, we must store coefficients, etc. We consider functions of one variable, and show that for some special neurons (corresponding to wavelets), neural networks are optimal approximators in the sense that they require (asymptotically) the smallest possible number of bits.<<ETX>>

On interval weighted three-layer neural networks

When solving application problems, the data sets used to train a neural network may not be one hundred percent precise but are within a certain range. By representing data sets with intervals, one has interval neural networks. By analyzing the mathematical model, the authors categorize general three-layer neural network training problems into two types. One of them can be solved by finding numerical solutions of nonlinear systems of equations. The other can be transformed into nonlinear optimization problems. Reliable interval algorithms such as interval Newton/generalized bisection method and interval branch-and-bound algorithm are applied to obtain optimal weights for interval neural networks. Applicable state-of-art interval software packages are also reviewed.

Network of Multi-Agent Traffic Controllers

Driving through streets of an inner city such as a downtown area sometimes can be frustrating. One might have to wait for a traffic light to turn green at an intersection where there is no car on the cross street. Or, there may be a lot of cars on the cross street that must be cleared in order to make the traffic flowing. The objective of this project is to develop an intelligent traffic controller model to coordinate a network of traffic lights such that the flow of the traffic is maximized and the time of the traffic flow is minimized. We proposed to develop a model that implements multi-agents and fuzzy controllers on a network of computers. In the model, we created two types of agents, communication and computation agents for each traffic light at an intersection. In order to validate our model, we created a simulation test bed utilizing a cluster of computers where each node on the cluster represents traffic lights at an intersection. The simulation test bed also allows us to perform comparisons of our model to the other models.