• 전기의세계
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• 제18권6호
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• pp.9-22
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• 1969

This thesis has suggested a method of applying the Maximum Principle of Pontryagin to the optimal control of distributive electrical networks. In general, electrical networks consist of branches, nodes, sources and loads. The effective values of steady state currents and voltages are independent of time but only expressed as the functions of position. Moreover, most of the node voltages and branch currents are not predetermined, that is, initially unknown, and their inherent loop characteristics satisfy only Kirchhoff's current and voltage laws. The Maximum Principle, however, needs the initial fixed values of all state variables for its standand way of application. In spite of this inconsistency this thesis has undertaken to suggest a new approach to the successful solution of the above mentioned networks by introducing scaling factors and a state variable change technique which transform the boundary-value unknown problem into the boundary-value partially fixed and partially free problem. For the examples of applying the method suggested, the control problems for minimizing copper quantity in a distribution line have been solved with voltage drop constraint imposed on. In the case of uniform load distribution it has been shown that the optimal wire diameter of the distribution line is reciprocally proportional to the root of distance. For the same load pattern as above the wire diameter giving the minimum copper loss in the distribution line has been shown to be reciprocally proportional to distance.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.185-220
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• 2016

We study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator defined on the half plane. Next, we establish a principle of maximum for the singular partial differential operator $${\Delta}_{\alpha}={\frac{{\partial}^2}{{\partial}r^2}+{\frac{2{\alpha}+1}{r}{\frac{\partial}{{\partial}r}}+{\frac{{\partial}^2}{{\partial}x^2}}+{\frac{{\partial}^2}{{\partial}t^2}}};\;(r,x,t){\in}]0,+{\infty}[{\times}{\mathbb{R}}{\times}]0,+{\infty}[$$. Later, we define the Littlewood-Paley g-function and using the principle of maximum, we prove that for every $p{\in}]1,+{\infty}[$, there exists a positive constant $C_p$ such that for every $f{\in}L^p(d{\nu}_{\alpha})$, $${\frac{1}{C_p}}{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}{\leqslant}{\parallel}g(f){\parallel}_{p,{\nu}_{\alpha}}{\leqslant}C_p{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}$$.

• ETRI Journal
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• 제30권1호
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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.

• 한국정밀공학회지
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• 제15권6호
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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.

• Nuclear Engineering and Technology
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• 제5권2호
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• pp.115-131
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• 1973

L.S. Pontryagin의 Maximum Principle과 수직방향을 고려하지 않은 2군 화산 방정식을 우라늄농축도 범위에 제한없이 원통형원자로의 최소 임계질량문제에 적용하였다. 핵연료 장전방법에 관한한 최적 원자로는 내심부와 외심부가 최소의 농축도를 갖고 중간영역은 최대의 농축도를 갖는 3-영역식 원자로인 것으로 밝혀졌다. 상기 3-영역식 원자로를 모델로 하여 임계조건을 유도하였으며, 또한 고리원자로를 예로하여 농축도를 여러가지로 변환시키면서 임계조건의 해를 구하는 수치해석을 수행하였다. 그 결과 여러가지 임계조건중 최소의 임계질량을 갖는 경우는 중간영역에서의 최대 농축도가 1.2%이고 내심부와 외심부에서의 농축도가 0.65%일때라는 것이 판명되었다.

• 대한수학회논문집
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• 제5권1호
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• pp.119-122
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• 1990

• 대한수학회지
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• 제10권2호
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• pp.73-75
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• 1973

• 대한전기학회:학술대회논문집
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• 대한전기학회 1985년도 하계학술회의논문집
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• pp.155-157
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• 1985

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.49-64
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• 2007

In this paper, we investigate optimal policies for three age-dependent populations in a competition system, which is controlled by fertility. By using Dubovitskii-Milyutin's general theory, the maximum principles are obtained for problems with free terminal states, infinite horizon and target sets, respectively.

• Nuclear Engineering and Technology
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• 제21권3호
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• pp.193-204
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• 1989

본 논문에서는 정보 이론의 maximum entropy Principle을 이용하여 중성자속 분포를 재생하는 새로운 방법을 시도하였다. 어떤 대상에 대한 부분적인 정보가 있을 때, 이 정보의 한도 내에서 entropy를 최대화시키는 확률 분포는 가장 객관적인 것이 된다. Nodal method계산결과인 평균 중성자속과 current의 값을 prior information으로 삼고, 핵 연료 집합체의 경계에서의 중성자속 분포를 확률의 형태로 변환해서 확률로써 다룬다. Prior information의 한도 내에서 entropy를 최대화시키는 경계에서의 확률 분포를 구하면 핵연료 집합체의 경계에서의 중성자속 분포가 구해지는데, 이것을 경계조건으로 heterogeneous assembly calculation을 행하여 세부적인 중성자속 분포를 구한다. 이 새로운 방법을 몇 개의 benchmark problem assembly에 응용해 본 결과, 노심의 안쪽 부분에서는 이 방법이 form function method에 의한 것과 비슷한 정확도를 보였고 바깥 부분에서는 다소 큰 오차를 보였다. 본 논문에서는 surface-averaged neutron current를 prior in-formation에 포함시키지 못했는데, 이것을 포함시키면 결과가 훨씬 개선 될 것으로 보인다.