• Journal of the Korean Mathematical Society
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• v.52 no.3
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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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• v.34 no.5
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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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• v.21 no.3
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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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• 1992.10a
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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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• v.28 no.5
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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.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.12 no.1
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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.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.5
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• pp.17-23
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• 1976

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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• v.40 no.3_4
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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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• v.4 no.1
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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.

• Journal of Energy Engineering
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• v.5 no.1
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• pp.87-92
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• 1996

This paper formulates dynamic optimization model for Time-Of-Use Rates when a electric power system consists of three generators and a rating period is divided into three sub-periods. We use Pontryagin's Maximum Principle to derive optimal price and investment policy. Particularly the cross-price elasticities of demand are considered in the objective function. We get the following results. First, the price is equal to short-run marginal cost when the capacity is sufficient. However, if the capacity constraint is active, the capacity cost is included in the price. Therefore it is equal to the long-run marginal cost. Second, The length of rating period affects allocation of capacity cost for each price. Third, the capacity investment in dynamic optimization is proportional to the demand growth rate of electricity. However the scale of investment is affected by not only its own demand growth rate but also that of other rating period.