• Journal of Korean Society of Industrial and Systems Engineering
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• v.10 no.16
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• pp.113-119
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• 1987

A Multistage production-inventory model is developed for deteriorating items. The model is developed deterministic but time-varing demand pattern and instantaneous delivery. Deterioration rates are assumed to vary from period to period. Discrete version of Pontryagin's maximum principle is used to present the efficient alogrithm to solve this model easily. A numerical example is given to illustrate the derived results.

• Journal of the Korean Institute of Telematics and Electronics
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• v.11 no.3
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• pp.27-31
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• 1974

The maximum principle of Pontryagin provides the celebrated method to obtain the optimum control switching time and switching points on the nuclear reactor. The control trajectories transfered from its initial state to the target state are optimized based on time optioptimal control method with the given reactor parameters and the piecewise constant input values.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.6
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• pp.97-106
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• 1998

In this Paper, a fuel minimizing closed loop explicit inertial guidance algorithm for orbit injection of a rocket is developed. In the formulation, the fuel burning rate and magnitude of thrust are assumed constant. The motion of rocket is assumed to be subject to the average inverse-square gravity, but negligible effects from atmosphere. The optimum thrust angle to obtain a given velocity vector in the shortest time with minimizing fuel consumption is first determined, and then the additive thrust angle for targeting the final position vector is determined by using Pontryagin's maximum principle. To establish real time processing, many algorithms of onboard guidance software are simplified. The explicit guidance algorithm is simulated on the 2nd-stage flight of the N-1 rocket developed in Japan. The results show that the explicit guidance algorithm works well in the presence of the maximum $\pm$10% initial velocity and altitude errors, and exhibits better performance than the open-loop program guidance. The effects of the guidance cycle time are also examined.

• Journal of Biosystems Engineering
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• v.24 no.5
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• pp.445-452
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• 1999

This study was conducted to develop a searching algorithm for optimal daily temperature setpoint greenhouse. An algorithm using crop growth and energy models was developed to determine optimum crop growth environment. The results of this study were as follows: 1. Mathematical models for crop growth and energy consumption were derived to define optimal daily temperature setpoint. 2. Optimum temperature setpoint, which could maximize performance criterion, was determined by using Pontryagin maximum principle. 3. Dynamic control of daily temperature using the developed algorithm showed higher performance criterion than static control with fixed temperature setpoint. Performance criteria for dynamic control models were with simulated periodic weather data and with real weather data, increased by 48% and 60%, respectively.

• Proceedings of the Korea Water Resources Association Conference
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• 1989.07a
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• pp.95-101
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• 1989

본 논문의 목적은 하천수질 상태변수에 따른 수자원의 최적 활용을 위해 시뮬레이션 기법과 Pontryagin의 최대원리를 이용한 최적 제어기법을 적용한 후 비교 고찰함으로서 하천 수질 종합관리를 위한 모형을 연구하는데 있다. 실제 적용을 위해 도시하천인 무심천을 선정하여 현장 실측 및 실험실 분석을 통해 각종 수리. 수문인자와 수질인자를 산정하였다. 수자원의 효율적 관리를 위하녀 하천 수질 개선방안으로 시뮬레이션 기법과 최적 제어기법을 이용하여 각 하천 구간별 제어지점에서 우리나라 하천 환경 기준치를 만족할 수 있도록 분석하여 두방법의 결과를 비교 평가함으로써 하천 수질종합관리를 위한 모형의 신뢰성과 유용성을 입증하고자 한다.

• Journal of the Korea Society for Simulation
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• v.2 no.1
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• pp.55-66
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• 1993

Although the Pontryagin's maximum principle theory is widely applied in control problems, its contribution to the solution procedure have been restricted just to figure out the rough picture of true solutions, probably due to the complexity of the two-point boundary value problems. This paper discusses a numerical approach to solve the control problems in connection with the two -point boundary value problems. A model of labor management negotiation during a strike has been constructed and solved explicitly by us of DVCPR subroutine introduced in IMSL. The results have been turned out that the management is better increase wage very slowly during the strike period, while , on the labor side, it is more effective to show the high intensity of demonstration against the company at the outset and gradually decrease it.

• Proceedings of the Korea Society for Simulation Conference
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• 1993.10a
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• pp.3-3
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• 1993

Although tile Pontryagin's maxlmum principle theory is widely applied in control problems, its contribution to the solution procedure have been restricted just to figure out the rough picture of true solutions, probably due to the complexity of the two-point boundary value problems.This paper discusses the numerical approach to solve the control problems in connection with the two-point boundary value problems. A model of labor-management negotiatulon during a strike has been constructed and solved explicitly by use of DVCPR subroutine introduced in IMSL. The results have been turned out that the management is better increase wage very slowly during the strike period, while, on the labor side, it is more effective to show the high intensity of demonstration against the company at the outset and gradually decrease it.

• Microbiology and Biotechnology Letters
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• v.2 no.2
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• pp.63-77
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• 1974

The optimal operation problem of enzyme reactor of double inhibitions are dealt with Maximum Principle and Steepest Ascent Method. The operation policy of the intial concentration and amount of substrate, reaction time and the method of cross feed of substrate are determined in a system of reactor of constant volume add with cross feed of substrate. The policy for the soluble enzyme and the immobilized enzyme are greatly different from each other, and the performance index, the profit per unit time, of the latter are nearly twice greater than that of the former.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.8
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• pp.1487-1493
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• 2016

The susceptible, exposed, infectious, and recovered model (SEIR) is used extensively in the field of epidemiology. On the other hand, dissemination information among users through internet grows exponentially. This information spreading can be modeled as an epidemic. In this paper, we derive the mathematical model of SEIR in viral communication from the view of optimal control theory. Overall the methods based on classical calculus, In order to solve the optimal control problem, proved to be more efficient and accurate. According to Pontryagin's minimum principle (PMP) the Hamiltonian function must be optimized by the control variables at all points along the solution trajectory. We present our method based on the PMP and forward backward algorithm. In this algorithm, one should integrate forward in time for the state equations then integrate backward in time for the adjoint equations resulting from the optimality conditions. The problem is mathematically analyzed and numerically solved as well.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.11
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• pp.861-869
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• 1989

The optimization problems, based on Pontryagin's Maximum Principle, for minimizing (damping) Xenon spatial oscillations in Load Following operations of Pressurized Water Reactor (PWR) is presented. The optimization model is formulated as an optimal tracking problem with quadratic objective functional. The oen-group diffusion equations and Xe-I dynamic equations are defined as equality constraints. By applying the maximum principle, the original problem is decomposed into a single time problem with no constraints. The resultant subproblems are optimized by using the conjugate Gradient Method. The computational results show that the Xenon spatial oscillation is minimized, and the reactor follows the load demand of the electrical power systems while maintaining the desired power distribution.