• 제어로봇시스템학회논문지
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• 제21권1호
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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.

• 수산해양기술연구
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• 제58권3호
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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.

• 한국수학사학회지
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• 제21권3호
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• pp.31-52
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• 2008

무한(infinity)의 개념은 다른 과학적 개념들과 마찬가지로 진화의 역사를 지닌 개념이다. 우리는 여기에서 볼짜노(Bolzano)를 중심으로 논의를 전개하고자 하는데, 그는 형이상학적 관점에서가 아니라 수학적으로 실무한(actual infinity)을 수용한 최초의 인물로 여겨지기 때문이다. 볼짜노는 현대의 플라톤주의자들처럼 구성(construction)과정과는 무관하게 무한집합(infinite set)을 그 자체로 옹호하였는데, 이는 내포(comprehension)의 원리와 모든 개념에 대한 외연의 유일성(unicity)에 근거한다. 또한 그는 무한집합과 그 부분 사이에 1:1 대응(one-to-one correspondence)이 성립한다는 사실을 역설로 보지 않고 무한집합의 특징으로 인식했다. 그리스 시대에는 단 하나의 무한의 존재만 인정한 데 반해 그는 여러 종류의 무한의 존재를 인정했으며, 무한에 대한 논리적 정의를 수립하였다. 무한의 문제는 수학에서 점증하는 중요성을 지닌 구성적 방법(constructive method)의 시금석이 된다. 여기에서는 이에 대한 운을 떼는 것으로 그치고 본격적인 연구는 차후의 과제로 남겨두겠다.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권4호
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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.

• 한국학교수학회논문집
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• 제10권1호
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• pp.91-111
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• 2007

본 연구는 컴퓨터를 활용하여 동적이며 직관적인 시각화 자료를 활용하여 실험에 참가한 고등학교 학생들의 수열 개념에 대해서 수열의 합 공식에 대해 귀납 추론으로 공식을 학생 스스로가 추론할 수 있는지를 알아보고자 했다. 학생들은 스스로가 수열의 합 공식을 사용하지 않고 귀납 추론으로 공식을 유도할 수 있음을 보았다. 또한 무한급수에서의 무한의 오개념인 잠재적 무한의 개념을 가진 학생들이 본 실험 자료로 학습을 하였을 때에 무한의 올바른 개념인 실 무한의 개념을 이해하는데 도움을 주는지에 대하여 연구를 하였는데 실험에 참가한 실험 학생들은 잠재적 무한 개념을 가지고 있었고 동적이고 직관적인 시각화 자료를 가지고 수업 후 실 무한의 개념으로의 변화가 있었다. 이들 학생들은 또한 컴퓨터를 활용하여 동적이고 직관적인 시각화 자료에 대해서 매우 흥미를 느꼈고, 수학에 대한 태도에도 영향을 주었다.

• 한국수학교육학회지시리즈A:수학교육
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• 제39권1호
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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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• 제4권2호
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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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• 제2권1호
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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.

• 한국수학사학회지
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• 제14권1호
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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.

• 한국통신학회논문지
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• 제37A권11호
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• pp.1001-1011
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• 2012

본 논문에서는 IEEE 802.11 시스템에서 경쟁 중인 터미널 수를 추정하고 이를 반영할 때 시스템 성능에 미치는 영향을 분석한다. IEEE 802.11 시스템에서는 터미널간의 다중 접근의 방법으로 DCF (Distributed Coordination Function)를 이용하고 있으며 경쟁하는 터미널 수를 정확하게 추정하여 반영하는 것이 시스템 throughput 증가하는데 중요한 요소가 된다. 본 논문에서는 터미널 수를 추정하는 방법으로 노이즈 정보가 필요하지 않는 Extended H Infinity Filter (EHIF)를 이용하여 터미널 수를 추정하는 방법을 제안한다. 경쟁하는 터미널의 수가 saturated되는 경우와 non-saturated되는 네트워크 환경에서 EHIF가 기존의 Extended Kalman Filter (EKF) 방법보다 좋은 성능을 가짐을 모의실험을 통해 확인하였고 이를 정량적으로 분석하였다.