• Journal of the Institute of Electronics Engineers of Korea SC
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• v.38 no.4
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• pp.11-19
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• 2001

In this paper, we study the convergence property of iterative learning control (ILC). First, we present a new method to prove the convergence of ILC using sup-norm. Then, we propose a new type of ILC algorithm adopting intervalized learning scheme and show that the monotone convergence of the output error can be obtained for a given time interval when the proposed ILC algorithm is applied to a class of linear dynamic systems. We also show that the divided time interval is affected from the learning gain and that convergence speed of the proposed learning scheme can be increased by choosing the appropriate learning gain. To show the effectiveness of the proposed algorithm, two numerical examples are given.

• The KIPS Transactions:PartA
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• v.11A no.2
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• pp.203-206
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• 2004

Wegmann's method has been known as the most efficient one for the Theodorsen equation that is needed to solve conformal mapping. It was researched in the earlier studies (1). However divergence was revealed in some difficult problems by numerical experiment using Wegmann's method. We analyzed the cause of divergence and proposed an improved method by applying a low frequency pass filter to Wegmann's method. Numerical experiments using the improved method showed convergence for all divergent problems using the Wegmann's method. In this paper, we prove theroretically the cause of convergence in the Numerical experiment using the improved method by applying a low frequency pass filter to Wegmann's method. We make use of Fourier transforms in this theoretical proof of convergence.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.11a
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• pp.419-422
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• 2002

저자는 등각사상을 추하기 위한 기존의 여러 Theodorsen 방정식의 해법 중 가장 유효한 해법으로 알려져 있는 Wegmann의 방법을 다룬바 있다. Wegmann의 방법으로 수치실험을 한 결과 난이도가 높다고 예상되는 문제에 있어 수렴했다가 발산을 하는 불안정현상이 나타났으며 수렴하지 않는 불안정현상의 원인을 분석하여 저주파필터를 적용한 새로운 반복법을 제안하여 Wegmann 방법으로는 발산하는 모든 문제에 있어서 수렴하는 수치실험 결과를 얻었다[1]. 본 논문에서는 저주파필터를 적용한 해법에 의해 수치적으로 수렴한 결과를 이론적으로 증명한다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.261-264
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• 2002

이 논문에서는 구간 수의 값을 갖는 함수들의 쇼케이적분을 생각하고자 한다. 이러한 구간 수의 값을 갖는 함수들의 성질들을 조사하여 오토연속인 퍼지측도에 관련된 쇼케이적분에 대한 수렴성 정리를 증명한다.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.473-486
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• 1998

A numerically stable technique to remove the limitation in choosing a shift in the subspace iteration method with shift is presented. A major difficulty of the subspace iteration method with shift is that because of singularity problem, a shift close to an eigenvalue can not be used, resulting in slower convergence. This study solves the above singularity problem using side conditions without sacrifice of convergence. The method is always nonsingular even if a shift is an eigenvalue itself. This is one of the significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shift, and the operation counts of above two methods are almost the same when a large number of eigenpairs are required. To show the effectiveness of the proposed method, two numerical examples are considered.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.371-383
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• 1999

An efficient and numerically stable eigensolution method for structures with multiple natural frequencies is presented. The proposed method is developed by improving the well-known subspace iteration method with shift. A major difficulty of the subspace iteration method with shift is that because of singularity problem, a shift close to an eigenvalue can not be used, resulting in slower convergence. In this paper, the above singularity problem has been solved by introducing side conditions without sacrifice of convergence. The proposed method is always nonsingular even if a shift is on a distinct eigenvalue or multiple ones. This is one of the significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shift, and the operation counts of above two methods are almost the same when a large number of eigenpairs are required. To show the effectiveness of the proposed method, two numerical examples are considered.

• The KIPS Transactions:PartB
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• v.14B no.7
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• pp.541-548
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• 2007

Due to the mathematical convergence property, Simulated Annealing (SA) has been one of the most popular optimization algorithms. However, because of its problem of slow convergence in the practical use, many variations of SA like Fast SA (FSA) have been developed for faster convergence. In this paper, we propose and prove that Greedy SA (GSA) also finds the global optimum in probability in the continuous space optimization problems. Because the greedy selection does not allow the cost to become worse, GSA is expected to have faster convergence than the conventional FSA that uses Metropolis selection. In the computer simulation, the proposed method is shown to have as good performance as FSA with Metropolis selection in the viewpoints of the convergence speed and the quality of the found solution. Furthermore, the greedy selection does not concern the cost value itself but uses only dominance of the costs of solutions, which makes GSA invariant to the problem scaling.

• Proceedings of the Korean Information Science Society Conference
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• 2007.06c
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• pp.303-308
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• 2007

최근에 제안된 감독 지식을 융합하는 강화 학습 기법인 potential-based RL 기법의 효용성은 이론적 최적 정책으로의 수렴성 보장으로 증명되었고, policy-reuse RL 기법의 우수성은 감독지식을 융합하지 않는 기존의 강화학습과 실험적인 비교를 통하여 증명되었지만, policy-reuse RL 기법을 potential-based RL 기법과 비교한 연구는 아직까지 제시된 바가 없었다. 본 논문에서는 potential-based RL 기법과 policy-reuse RL 기법의 실험적인 성능 비교를 통하여 기법이 policy-reuse RL 기법이 policy-reuse RL 기법에 비하여 더 빠르게 수렴한다는 것을 보이며, 또한 policy-reuse RL 기법의 성능은 재사용하는 정책의 optimality에 영향을 받는다는 것을 보인다.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.1
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• pp.9-14
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• 2008

This paper presents an observer design methodology for a special class of multi input multi output(MIMO) nonlinear systems. First, we characterize the class of MIMO nonlinear systems with a triangular structure. Also, the observability matrices that plays an important role in proving the convergence of the proposed observer are generalized to MIMO systems. By using the generalized observability matrices, it is shown that under the boundedness conditions of system state and input, the proposed observer guarantees the local exponential convergence to zero of the estimation error.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.10a
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• pp.127-127
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• 1993

Separating Hyperplane의 기하학적인 성질을 이용하여, 일반적인 Closed Convex Set들의 교집합에 속하는 점을 찾아가는 방법을 제안하고, 교집합에 속하는 점을 찾아가는 과정에서 그 교집합의 공집합 여부를 판정할 수 있는 방법을 제안하였다. 이 기법은 기존의 방법들이 가정하는 수렴조건보다 더 일반적인 조건 하에서도 수렴성을 갖는 것을 증명할 수 있었으며, 그 교집합의 공집합 여부를 선형부동식 해의 존재 유무로 판정할 수 있는 방법을 제시하였다. 몇가지 특수한 경우의 Convex Set들의 경우에 대한 기법의 적용 결과도 알아 보기로 한다.