• Journal of Institute of Control, Robotics and Systems
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• v.21 no.1
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• pp.14-20
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• 2015

This paper describes the design of a robust H-infinity attitude controller for a quad-rotor. The linear model of a quad-rotor was estimated using PEM (Prediction Error Minimization) method with experimental input and output data. To design an attitude controller, an extended plant was constructed by adjusting several uncertainties and weighting functions. An H-infinity controller was obtained by applying H-infinity methodology to the extended plant. Through frequency-domain analysis, it was shown that the designed controller can overcome uncertainties up to 75% of the plant model. The performance and robustness of the controller were verified through time-domain simulation.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.58 no.3
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• pp.241-250
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• 2022

This paper describes the design of H-infinity controller for robust control of a DC motor system. The suggested controller can ensure robustness against disturbance and model uncertainty by minimizing H-infinity norm of the transfer function from exogenous input to performance output and applying the small gain theorem. In particular, the controller was designed to reduce the effects of disturbance and model uncertainty simultaneously by formalizing these problems as a mixed sensitivity problem. The validity of the proposed controller was demonstrated by computer simulations and real experiments. Moreover, the effectiveness of the proposed controller was confirmed by comparing its performance with PI controller, which was tested under the same experimental condition as the H-infinity controller.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.31-52
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• 2008

The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not just from a metaphysical perspective but from a mathematical one. Like modem platonists, Bolzano defended the infinite set itself regardless of the construction process; this is based on the principal of comprehension and unicity of denotation regarding all concepts. In addition, instead of considering as paradoxical the fact that a one-to-one correspondence existed between an infinite set and its parts, he regarded it in a positive way as a special characteristic. While the Greek era recognized the existence of only one infinity, Balzano acknowledged the existence of various types of infinity and formulated a logical definition for it. The question of infinity is a touchstone of constructive method which holds an increasingly important role in mathematics. The present study stops with just a brief reference to the subject matter and we will leave further in-depth investigation for later.

• The Mathematical Education
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• v.47 no.4
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• pp.447-465
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• 2008

The purpose of this study is to suggest effective teaching methods on the concept of infinity for students to obtain the right concept in the middle school curriculum. Many people have thought that infinity is something vouge and unapproachable. But, nowadays it is rather something with a precise definition that lies at the core of modern mathematics. To understand mathematics and science very well, it is necessary to comprehend the concept of infinity. But students tend to figure out the properties of infinite objects and limit concepts only through their experience closely related to finite process, and so they are apt to have their spontaneous intuition and misconception about it. Since most of them have cognitive obstacles in studying the infinite concepts and misconception, mathematics teachers need to help them overcome the obstacles and establish the right secondary intuition for the concepts through good examples and appropriate explanation. In this study, we consider the developing process of the concept of infinity in human history and give some comments and suggestions in teaching methods relative to that concept with new suitable examples.

• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.91-111
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• 2007

This study investigated how high school students predict the rule, the sum of sequence for the concept of sequence, for the given patterns based on inductive approach using computers that provide dynamic functions and materials that are visual. Students for themselves were able to induce the formula without using the given formula in the textbook. Furthermore, this study examined how these technology and materials affect students' understanding of the concept of actual infinity for those who have the concept of the potential infinity which is the misconception of infinity in a infinity series. This study shows that students made a progress from the concept of potential infinity to that of actual infinity with technology and materials used I this study. Students also became interested in the use of computer and the visualized materials, further there was a change in their attitude toward mathematics.

• The Mathematical Education
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• v.39 no.1
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• pp.37-47
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• 2000

Number concept is basic in mathematics education. But it is very complex and is not easy to understand real number concept, because of its infinity. This study tried to show that what percents of secondary school mathematics teachers in Korea understood the properties of real number, such as cardinality, continuity, relation with real line, and infinity, which were written by verbal language.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.130-139
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• 2002

In this paper, at first, we investigate existing algorithms for finding the minimum infinity-norm solution of consistent linear equations and then propose a new algorithm. The proposed algorithm is intended to includes the advantages of computational efficiency as well as geometric explicitness. As a practical application example, optimum trajectory planning for redundant robot manipulators is considered. Also, an efficient approach avoiding discontinuity in trajectory is proposed by resolving the non-uniqueness problem of minimum infinity-norm solution. To be specific, the proposed method for checking possible discontinuity does not need any other algorithms in checking the possibility of discontinuity while previous work needs specially designed checking courses. To show the usefulness of the proposed techniques, an example calculating minimum infinity-norm solution for comparing the computational efficiency as well as the trajectory planning for a redundant robot manipulator are included.

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.23-38
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• 2004

We proposed the infinity control principle to evaluate the Biological function. The H infinity control was applied to the Sodium (Na) ion selective gating channel on the excitable cellular membrane of the neural system. The channel opening, closing and inactivation processes were expressed by movements of three gates and one inactivation blocking particle in the channel pore. The rate constants of the channel state transition were set to be voltage dependent. The temporal changes in amounts per unit membrane area of the channel states were expressed by means of eight differential equations. The biochemical mimetic used to complete the Na ion selective channel was regarded as noise. The control inputs for ejecting the blocking particle with plugging in the channel pore were set for the active transition from inactivated states to a closed or open state. By applying the H infinity control, we computed temporal changes in the channel states, observers, control inputs and the worst case noises. The present paper will be available for evaluating the noise filtering function of the biological signal transmission system.

• Journal for History of Mathematics
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• v.14 no.1
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• pp.41-46
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• 2001

In the western culture, the definition of infinity and finiteness developed into various features, being combined with classical Hebraism and Hellenism, and after modernism, it has been paralleled with natural sciences within the circle of its tradition, whereas the definition of infinity has been showed in Buddhism, the traditional religion, which has been handed down without scientific consideration, in the eastern culture. This is the most notable characteristics between two hemispheres. In this paper, I will show sameness and differences of these two cultures in terms of defining infinity. Also in terms of examining the definition of infinity and finiteness in the Buddhist principles which has been handed down since 600∼500 B.C. I will show how the definition of Buddhist infinity connect with the mathematical definition of today.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.11
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• pp.1001-1011
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• 2012

In this paper, the effects to system performance are evaluated in IEEE 802.11 system when the number of competing terminals are estimated and reflected to the system. The IEEE 802.11 system uses DCF (Distributed Coordination Function) for the multiple access method, and the system throughput performance depends on the accuracy of the estimated number of competing terminals. We propose extended H infinity filter (EHIF) approach which does not require the noise information for estimating the number of competing terminals. Simulation results show that EHIF outperforms the extended Kalman filter in both saturated and non-saturated network conditions.