• 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.

• 전기의세계
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• v.28 no.6
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• pp.47-51
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• 1979

An optimal problem in which the dynamics is nonlinear and the cost functional includes a discontinuous integrand is investigated. By using Neustadt's abstract maximum principle, a necessary conditions in the form of Pontryagin's maximum principle is derived and it is further shown that this necessary condition is also a sufficient condition for normal problems with linear-in-the-state systems.

• ETRI Journal
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• v.30 no.1
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• pp.81-88
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• 2008

The security threat posed by worms has steadily increased in recent years. This paper discusses the application of the optimal and sub-optimal Internet worm control via Pontryagin's maximum principle. To this end, a control variable representing the optimal treatment strategy for infectious hosts is introduced into the two-factor worm model. The numerical optimal control laws are implemented by the multiple shooting method and the sub-optimal solution is computed using genetic algorithms. Simulation results demonstrate the effectiveness of the proposed optimal and sub-optimal strategies. It also provides a theoretical interpretation of the practical experience that the maximum implementation of treatment in the early stage is critically important in controlling outbreaks of Internet worms. Furthermore, our results show that the proposed sub-optimal control can lead to performance close to the optimal control, but with much simpler strategies for long periods of time in practical use.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.857-871
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• 2022

In this work, we formulated a mathematical model for divorce in marriage and extended in to an optimal control model. Firstly, we qualitatively established the model positivity and boundedness. Also we saw sensitivity analysis of the model and identified the positive and negative indices parameters. An optimal control model were developed by incorporating three time dependent control strategies (couple relationship education, reducing getting married too young & consulting separators to renew their marriage) on the deterministic model. The Pontryagin's maximum principle were used for the derivation of necessary conditions of the optimal control problem. Finally, with Newton's forward and backward sweep method numerical simulation were performed on optimality system by considering four integrated strategies. So that we reached to a result that using all three strategies simultaneously (the strategy D) is an optimal control in order to effectively control marriage divorce over a specified period of time. From this we conclude that, policymakers and stakeholders should use the indicated control strategy at a time in order to fight against Divorce in a population.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.219-231
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• 2003

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by taking E(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.

• 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.

• Nuclear Engineering and Technology
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• v.5 no.2
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• pp.115-131
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• 1973

L.S. Pontryagin's maximum principle is applied to the minimum critical mass problem without any restriction on the ranges of uranium enrichment. For the analysis, two group diffusion equation is adopted for a cylindrical reactor neglecting the vertical axis consideration. The result shows that the three-zoned reactor turns out to be most optimal: the inner and outer zones with the minimum enrichment ; whereas the middle 3one with the maximum enrichment. With the given three-zoned reactor, critical condition is derived, which leads to the calculation of the determinant. By finding the roots of the determinant the numerical calculation of the minimum critical mass is carried out for the case of Kori reactor geometry changing the minimum or the maximum enrichment. It is found from many computed values that the least possible critical mass turns out to be the case of 1.2% maximum enrichment for the middle zone and 0.65% minimum enrichment for the inner and out zones.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.5
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• pp.57-68
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• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• 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.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.355-369
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• 2004

The paper determines by control-theoretic means the optimal dose of fertilizer to be used to two plants for maintaining optimal revival of their growths, which are retarded mainly due to the toxicity contributed by the plants jointly.