• 대한수학회지
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• 제52권3호
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• pp.469-487
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• 2015

We consider a model of HIV infection with various compartments, including target cells, infected cells, viral loads and immune effector cells, to describe HIV type 1 infection. We show that the proposed model has one uninfected steady state and several infected steady states and investigate their local stability by using a Jacobian matrix method. We obtain equations for adjoint variables and characterize an optimal control by applying Pontryagin's Maximum Principle in a linear control problem. In addition, we apply techniques and ideas from linear optimal control theory in conjunction with a direct search approach to derive on-off HIV therapy strategies. The results of numerical simulations indicate that hybrid on-off therapy protocols can move the model system to a "healthy" steady state in which the immune response is dominant in controlling HIV after the discontinuation of the therapy.

• East Asian mathematical journal
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• 제34권5호
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• pp.683-691
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• 2018

We consider an optimal control problem for an impulsive stage-structured model involving ordinary differential equations with impulsive values of initial conditions in the next year. The main goal is to maximize a profit of the catch of Pacific cod in the South Korea through optimal harvest strategy as a control of adult cod. We established necessary conditions for the optimal harvest control using idea of Pontryagin's maximum principle. The optimal harvest strategy is to numerically solve the equation by using an iterative method with the Runge-Kutta method. Finally, we compare a monthly average of fishing mortality of Pacific cod from 2013 to 2017 with monthly fishing mortality for result obtained optimal harvest strategy.

• 전기의세계
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• 제21권3호
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• pp.48-52
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• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.941-946
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• 1992

Three different reflux policies are compared for a batch distillation process in which a fixed recovery with a given average purity of the distillate is required ; the first, for the constant distillate purity ; the second, for the constant reflux ratio ; finally, for the optimal reflux policy which gives the minimum operation time. The optimal reflux policy was obtained using pontryagin's maximum principle. Througy the numerical simulations for the three different binary mixtures, it was found that the time advantage of the optimal reflux operation over the constant overhead composition operation varies form 10.0 to 22.4% and the advantage over the constant reflux operation varies from 1106 to 36.6% in the three cases considered.

• ETRI Journal
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• 제28권5호
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• pp.692-695
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• 2006

Recently, there has been a constant barrage of worms over the Internet. Besides threatening network security, these worms create an enormous economic burden in terms of loss of productivity not only for the victim hosts, but also for other hosts, as these worms create unnecessary network traffic. Further, measures taken to filter these worms at the router level incur additional network delays because of the extra burden placed on the routers. To develop appropriate tools for thwarting the quick spread of worms, researchers are trying to understand the behavior of worm propagation with the aid of epidemiological models. In this study, we present an optimization model that takes into account infection and treatment costs. Using this model we can determine the level of treatment to be applied for a given rate of infection spread.

• 대한설비공학회지:설비저널
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• 제12권1호
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• pp.2-11
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• 1983

The solar energy retention rate of a flat plate collector can be increased by increasing water flow rate through the collector which also increases the pumping energy incurred in obtaining that solar energy. The problem of optimal flow rate is formulated to fit within the framework of pontryagin's maximum principle and with a few simplifying assumptions, an optimal solution that can be easily implemented is obtaincd, The optimal solution is used in the simulation of a solar heating system using actual climatological data and the results are compared with that of on-off control. The result that not only the object function but, In some cases, also the solar energy retention rate the collector is increased. In is also found that the optimal control gets more advantageous as the solar insolation level gets lower, and also as tile cost of auxiliary heating fuel gets higher.

• 대한전자공학회논문지
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• 제13권5호
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• pp.17-23
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• 1976

고속열중성자로에서 정상 운전중인 원자로를 운전정지하였다가 재가동할 때 가장 문제가 되는 것은 핵분열 생성물인 Xe135의 독소작용이다. 이것은 Xe135가 원자로 출력에 영향을 주는 열중성자에 대한 흡수단면적이 크고 그의 반감기가 길기 때문이다. 그러므로 원자로의 일시적 운전정지가 요구될 때 이의 재가시에는 반듯이 이 독소를 능과할 수 있는 충분한 초과반응도를 가해 주던지, Xe135가 붕괴되어 그의 농도가 줄어든 이후에야 원자로의 재가동이 가능하게 된다. 위와 같은 문제는 사실상 원자로 운전시 안전성 뿐만 아니라 경제성에도 큰 영향을 주고 있다. 본 논문에서는 이 점을 고려하여 Pontoyagin의 최대원리를 이용하여 운전정지를 최적화시키므로서 언제든지 원자로를 전출력으로 재가동할 수 있도록 운전정지 방법을 개선하였다. 그러나 제어과정에서나 그 이후에도 X, 농도는 제어된 허용치를 넘지 않고 최소시간 이내에 모든 제어를 끝내도록 하였다. The buildup of fission product, i.e. Xe-135 poisoning, is a prime factor in restarting a nuclear reactor from the shutdown, which was under normal operation in the high flux thermal reactor, It is caused by the high absorption crosssection of Xe-135 to thermal neutrons and its long half life, from which the thermal power is affected. It is then possible to restart a nuclear reactor after the sufficient excess reactivity to override this poisoning must be inserted, or its concentration is decreased sufficiently when its temporary shutdown is required. As ratter of fact, these have an important influence not only on reactor safety but also on economic aspect in operation. Considering these points in this study, the shutdown process was cptimized using the Pontryagin's maximum principle so that the shutdown mirth[d was improved as to restart the reactor to its fulpower at any time, but the xenon concentration did not excess the constrained allowable value during and after shutdown, at the same time all the control actions were completed within minimum time from beginning of the shutdown.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.633-656
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• 2022

Many regions of the world are now facing the second wave of boomed cases of COVID-19. This time, the second wave of this highly infectious disease (COVID-19) is becoming more devastating. To control the existing situation, more mass testing, and tracing of COVID-19 positive individuals are required. Furthermore, practicing to wear a face mask and maintenance of physical distancing are strongly recommended for everyone. Taking all these into consideration, an optimal control problem has been reformulated in terms of nonlinear ordinary differential equations in this paper. The aim of this study is to explore the control strategy of coronavirus-2 disease (COVID-19) and thus, minimize the number of symptomatic, asymptomatic and infected individuals as well as cost of the controls measures. The optimal control model has been analyzed analytically with the help of the necessary conditions of very well-known Pontryagin's maximum principle. Numerical simulations of the optimal control problem are also performed to illustrate the results.

• Ocean Systems Engineering
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• 제4권1호
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• pp.63-82
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• 2014

Declutching control is applied to a hemispherical wave energy converter with direct linear electric Power-Take-Off systems oscillating in heave direction in both regular and irregular waves. The direct linear Power-Take-Off system can be simplified as a mechanical spring and damper system. Time domain model is applied to dynamics of the hemispherical wave energy converter in both regular and irregular waves. And state space model is used to replace the convolution term in time domain equation of the heave oscillation of the converter due to its inconvenience in analyzing the controlled motion of the converters. The declutching control strategy is conducted by optimal command theory based on Pontryagin's maximum principle to gain the controlled optimum sequence of Power-Take-Off forces. The results show that the wave energy converter with declutching control captures more energy than that without control and the former's amplitude and velocity is relatively larger. However, the amplification ratio of the absorbed power by declutching control is only slightly larger than 1. This may indicate that declutching control method may be inapplicable for oscillating wave energy converters with direct linear Power-Take-Off systems in real random sea state, considering the error of prediction of the wave excitation force.

• 에너지공학
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• 제5권1호
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• pp.87-92
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• 1996

본 연구는 전력계통이 3개의 발전기로 구성되었고, 요금적용 시간대가 3개인 경우 동태적 최적화를 이용한 최적 가격 및 투자 정책을 도출하기 위한 것이다. 이를 위하여 최대원리법(Maximum Principle)을 이용하였으며, 종전에는 수요함수에서 고려되지 않았던 교차가격 탄력성을 수요함수에 포함시켰다. 분석 결과 다음과 같은 결론을 얻을 수 있다. 첫째, 설비가 충분한 경우 각 시간대의 최적 가격은 단기한계비용과 일치한다. 그러나 시간이 경과함에 따라 수요증가에 의하여 설비제약이 활성화되면 각 시간대의 가격은 설비비를 포함하는 장기한계비용 형태를 띄게 된다 둘째, 각 시간대에 있어서 발전기의 설비비의 분담은 요금적용 시간대의 길이에 의하여 영향을 받는다. 즉, 해당 시간대의 요금적용 시간대가 길어지면 길어질수록 해당시간대에 대응되는 설비의 설비비 분담은 감소하고, 짧아지면 질수록 설비분담은 높아지게 된다. 셋째, 동태적 분석에서의 설비투자는 기본적으로 각 시간대의 수요증가율과 같은 비율로 증가하며, 또한 신규설비 투자규모는 각 시간대의 투자설비를 서로 분담하게 된다.