• Journal of the Korean Society for Railway
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• v.13 no.4
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• pp.419-424
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• 2010

Through the process of state estimation in the electric railway substation, this paper presents a new method for improving the reliability of the measurements corrupted by gauge error. Unlike the case of commercial power systems, it has been difficult to perform the state estimation by using the usual methods in the electric railway substation. At some of the monitoring points in the substation, most often, it is hard to define the measurement functions by use of the states or as we set up a new states set with the change of system topology, some of the measurement functions become part of the states themselves, which leads to poor results. To resolve the problems in the existing method caused by the relations between the states and the measurement functions at the monitoring points, the proposed method in this paper exploits the equality constraints. They can be derived numerously and concisely from the current and the voltage attributes of the Scott transformer and the buses connecting conditions, etc. We have proofed the effectiveness of the proposed method by the test on a standard sample substation.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.587-602
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• 2003

본 논문에서는 벡터값을 가지는 함수로 이루어진 벡터 변분 부등식들의 해집합사이의 관계, 미분 불가능한 볼록함수로 이루어진 벡터 볼록 최적화 문제의 해집합들과 볼록함수의 아래미분으로 표현된 벡터 변분부등식의 해집합들과의 관계, 제약집합이 볼록 함수로 구체적으로 주어질 때의 벡터 변분부등식의 해가 될 필요 충분조건, 섭동된 강 단조 벡터 변분부등식의 안정성 결과와 섭동된 벡터 강 볼록 최적화문제에의 적용에 대한 최근 연구 결과를 정리한다.

• Journal of the Korean Data and Information Science Society
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• v.6 no.2
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• pp.17-27
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• 1995

We propose a framework for representing and processing uncertain knowledge on the basis of constraint satisfaction. A system of equations and/or inequalities can be considered as a set of constraints that should be solved, and each constraint in the set is transformed into a corresponding logical formula which can be solved through a constraint solving program. Most of rule-based systems, for instance, use a simple probabilistic theory in order to maintain uncertain knowledge, therefore uncertain knowledge can be represented and processed in the constraint satisfaction program quite efficiently.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.5
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• pp.549-554
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• 2012

In this paper, we consider the optimal fuzzy filter of nonlinear discrete-time with estimation error variance constraint. First, the Takagi and Sugeno(T-S) fuzzy model is employed to approximate the nonlinear system. Next, the error state is mean square bounded, and the steady state variance of the estimation error of each state is not more than the individual predefined value. It is shown that, the addressed problem can be carried out by solving linear matrix inequality(LMI) and some algebraic quadratic matrix inequalities. Finally, some examples are provided to illustrate the design procedure and expected performance through simulations.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.10
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• pp.493-501
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• 2007

The imprecise real-time system provides flexibility in scheduling time-critical tasks. Most scheduling problems of satisfying both 0/1 constraint and timing constraints, while the total error is minimized, are NP-complete when the optional tasks have arbitrary processing times. Liu suggested a reasonable strategy of scheduling tasks with the 0/1 constraint on uniprocessors for minimizing the total error. Song et at suggested a reasonable strategy of scheduling tasks with the 0/1 constraint on multiprocessors for minimizing the total error. But, these algorithms are all off-line algorithms. In the online scheduling, the NORA algorithm can find a schedule with the minimum total error for the imprecise online task system. In NORA algorithm, EDF strategy is adopted in the optional scheduling. On the other hand, for the task system with 0/1 constraint, EDF_Scheduling may not be optimal in the sense that the total error is minimized. Furthermore, when the optional tasks are scheduled in the ascending order of their required processing times, NORA algorithm which EDF strategy is adopted may not produce minimum total error. Therefore, in this paper, an online algorithm is proposed to minimize total error for the imprecise task system with 0/1 constraint. Then, to compare the performance between the proposed algorithm and NORA algorithm, a series of experiments are performed. As a conseqence of the performance comparison between two algorithms, it has been concluded that the proposed algorithm can produce similar total error to NORA algorithm when the optional tasks are scheduled in the random order of their required processing times but, the proposed algorithm can produce less total error than NORA algorithm especially when the optional tasks are scheduled in the ascending order of their required processing times.

• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.