• Industrial Engineering and Management Systems
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• 제7권2호
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• pp.143-149
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• 2008

There have been some approximation analysis methods for a GI/G/1 queueing system. As one of them, an approximation technique for the steady-state probability in the GI/G/1 queueing system based on the iteration numerical calculation has been proposed. As another one, an approximation formula of the average queue length in the GI/G/1 queueing system by using the diffusion approximation or the heuristics extended diffusion approximation has been developed. In this article, an approximation technique in order to analyze the GI/G/1 queueing system is considered and then the formulae of both the steady-state probability and the average queue length in the GI/G/1 queueing system are proposed. Through some numerical examples by the proposed technique, the existing approximation methods, and the Monte Carlo simulation, the effectiveness of the proposed approximation technique is verified.

• 대한수학회논문집
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• 제10권3호
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• pp.715-733
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• 1995

We present a transient queue size distribution for $M/G/m/N$ queue with state dependent arrival rates, using the diffusion process with piecewise constant diffusion parameters, with state space [0, N] and elementary return boundaries at x = 0 and x = N. The model considered here contains not only many basic model but the practical models such as as two-node cyclic queue, repairmen model and overload control in communication system with finite storage buffer. For the accuracy check, we compare the approximation results with the exact and simulation results.

• 한국정밀공학회지
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• 제25권12호
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• pp.89-99
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• 2008

In this paper, the position tracking control problem of the servo system with nonlinear dynamic friction is issued. The nonlinear dynamic friction contains a directly immeasurable friction state variable and the uncertainty caused by incomplete parameter modeling and its variations. In order to provide the efficient solution to these control problems, we propose the composite control scheme, which consists of the robust friction state observer, the FNN approximator and the approximation error estimator with sliding mode control. In first, the sliding mode controller and the robust friction state observer is designed to estimate the unknown internal state of the LuGre friction model. Next, the FNN estimator is adopted to approximate the unknown lumped friction uncertainty. Finally, the adaptive approximation error estimator is designed to compensate the approximation error of the FNN estimator. Some simulations and experiments on the servo system assembled with ball-screw and DC servo motor are presented. Results show the remarkable performance of the proposed control scheme. The robust friction state observer can successfully identify immeasurable friction state and the FNN estimator and adaptive approximation error estimator give the robustness to the proposed control scheme against the uncertainty of the friction parameters.

• Coupled systems mechanics
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• 제4권1호
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• pp.1-18
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• 2015

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• Interaction and multiscale mechanics
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• 제7권1호
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• pp.525-542
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• 2014

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• 한국정보과학회논문지:소프트웨어및응용
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• 제30권11호
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• pp.1054-1061
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• 2003

강화학습의 대표적인 알고리즘인 Q-Learning은 상태공간의 모든 상태-행동 쌍(state-action pairs)의 평가값이 수렴할 때까지 반복해서 경험하여 최적의 전략(policy)을 얻는다. 상태공간을 구성하는 요소(feature)들이 많거나 요소의 데이타 형태가 연속형(continuous)인 경우, 상태공간은 지수적으로 증가하게 되어, 모든 상태들을 반복해서 경험해야 하고 모든 상태-행동 쌍의 Q값을 저장하는 것은 시간과 메모리에 있어서 어려운 문제이다. 본 논문에서는 온라인으로 학습을 진행하면서 비슷한 상황의 상태들을 클러스터링(clustering)하고 새로운 경험에 적응해서 클러스터(cluster)의 수정(update)을 반복하여, 분류된 최적의 전략(policy)을 얻는 새로운 함수근사(function approximation)방법인 Q-Map을 소개한다. 클러스터링으로 인해 정교한 제어가 필요한 상태(state)는 규칙(rule)으로 추출하여 보완하였다. 미로환경과 마운틴 카 문제를 제안한 Q-Map으로 실험한 결과 분류된 지식을 얻을 수 있었으며 가시화된(explicit) 지식의 형태인 규칙(rule)으로도 쉽게 변환할 수 있었다.

• 한국공작기계학회논문집
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• 제18권1호
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• pp.90-102
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• 2009

In this paper, a tracking control problem for a mechanical servo system with nonlinear dynamic friction is treated. The nonlinear friction model contains directly immeasurable friction state and the uncertainty caused by incomplete modeling and variations of its parameter. In order to provide the efficient solution to these control problems, we propose a hybrid control scheme, which consists of a robust friction state observer, a RFNN estimator and an approximation error estimator with sliding mode control. A sliding mode controller and a robust friction state observer is firstly designed to estimate the unknown infernal state of the LuGre friction model. Next, a RFNN estimator is introduced to approximate the unknown lumped friction uncertainty. Finally, an adaptive approximation error estimator is designed to compensate the approximation error of the RFNN estimator. Some simulations and experiments on the mechanical servo system composed of ball-screw and DC servo motor are presented. Results demonstrate the remarkable performance of the proposed control scheme.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.333-333
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• 2000

When the generalized singular perturbation method is used for model reduction, the state variables of the original system is reconstructed from the reduced order model. The state reduction error is defined, which shows how well the reconstructed state variables approximate the state variables of the original system equation.

• Bulletin of the Korean Chemical Society
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• 제27권8호
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• pp.1181-1185
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• 2006

By using two different computer simulation methods, of which one produces exact results while the other is based on the Wilemski-Fixman closure approximation, we evaluate the utility of closure approximation in calculating the rates of diffusion-controlled reactions involving a reactant with multiple reaction sites. We find that errors in the estimates of steady-state rate constants due to closure approximation are not so large. We thus propose an approximate analytic expression for the rate constant based on the closure approximation.

• 정보처리학회논문지D
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• 제11D권1호
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• pp.219-228
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• 2004

지금까지 비율(proportion)에 대한 신뢰구간의 근사적 추정량(approximate estimator)에 대한 여러 기법들이 제안되었으나, 시뮬레이션 결과에 대한 coverage 분석을 수행할 경우에는 정규분포에 기반 한 신뢰구간 추정량이 주로 이용되었다. 그 이유는 정규분포에 대한 근사법이 다른 근사법들 보다 실제 구현하는데 쉽게 여겨졌기 때문이다. 하지만, 최근에 arcsin 변환에 기반한 coverage 분석을 위한 근사법이 [12]에서 시뮬레이션 수행 시에 최종결과에 요구되는 정확도의 조절과 비율을 추정하기 위해서 사용되었다. 본 논문에서는 세 개의 신뢰구간 추정량 근사법(정규분포 기반 근사법, arcsin 변환 기반 근사법, 그리고 F-분포 기반 근사법)을 비교 분석하였다. 세 신뢰구간에 대한 추정량을 단일 프로세서와 다중 프로세서 상에서 참조모델(reference model)로 M/M/1/$\infty$와 W/D/l/$\infty$ 큐잉 시스템을 활용하여 정상상태(steady-state)에서의 평균치를 추정하는 시뮬레이션에 적용하였다.