• 대한수학회보
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• 제45권3호
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• 대한수학회지
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• 제43권5호
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• pp.931-950
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• 2006

We study the identification problems of constant parameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parameters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions [13].

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.947-951
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• 1989

A Class of nonlinear distributed parameter control problems is first stated in a partial differential equation form in multi-index notion and then converted into an integral equation form. Necessary conditions for optimality in the form of maximum principle are then derived in Sobolev space W$^{l}$, p/(1 leq. p .leq. .inf.)..

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.365-374
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• 2009

Under certain conditions, we use augmented Lagrangians to transform a class of generalized semi-infinite min-max problems into common semi-infinite min-max problems, with the same set of local and global solutions. We give two conditions for the transformation. One is a necessary and sufficient condition, the other is a sufficient condition which can be verified easily in practice. From the transformation, we obtain a new first-order optimality condition for this class of generalized semi-infinite min-max problems.

• 대한수학회지
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• 제47권1호
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• pp.17-28
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• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• Korean Journal of Mathematics
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• 제23권2호
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• pp.283-291
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• 2015

In the optimal control problem, at first we search the expected optimal solution by using Pontryagin type's necessary conditions called the maximum principle. Next we use the sufficient conditions to conclude that the searched solution is optimal. In this article the sufficient conditions are studied. The value function is used for sufficient conditions.

• East Asian mathematical journal
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• 제16권2호
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• pp.317-330
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• 2000

In this paper we consider the optimal control problem of both operators and parameters for nonlinear hyperbolic systems. For the identification problem, we show that for every value of the parameter and operators, the optimal control problem has a solution. Moreover we obtain the necessary conditions of optimality for the optimal control problem on the system.

• International Journal of Railway
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• 제2권2호
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• pp.70-79
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• 2009

An optimal driving strategy of a train in a long journey on a nonsteep track has four phases: an initial power phase, a long hold speed phase, a coast phase and a final brake phase. The majority of the journey is speed holding. On a track with steep gradients, it becomes necessary to vary the strategy around steep sections of track because it is not possible to hold a constant steep on steep track. Instead we must interrupt the speed hold phase with a power phase. The aim of this paper is to show that there is a unique power phase that satisfies the necessary conditions for an optimal journey. The problem is developed and solved for various cases, from a simple single steep gradient to a complicated multiple steep gradient section. For each case, we construct a set of new conditions for optimality of the power phase that minimises the energy used during the power phase subject to a weighted time penalty. We then use the new necessary conditions to develop a calculate scheme for finding an optimal power phase for a steep incline. We also present an example to confirm the uniqueness of an optimal power phase.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1043-1048
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• 1990

The degenerate case of multivariable hyperbolic distributed-parameter systems (systems of hyperbolic partial differential equations) in time coordinate t and space coordinate x is characterized by a property that all the characteristic curves of the state equations are parallel to the coordinate axes of independent variables. It is a disturbing fact, although not well known, that the so-called maximum principle as applied to these systems does not exist for the control that depend on time alone. In this paper, however, it is shown that a set of necessary conditions in the small can exist for unconstrained as well as magnitude constrained controls in a locally convex set. The necessary conditions thus derived can be used conveniently to find the optimal control for degenerate hyperbolic distributed-parameter control systems.

• 한국전산구조공학회논문집
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• 제13권4호
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• pp.417-425
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• 2000

본 연구에서는 이산성 연속형 최적성규준방법(DCOC)을 이용하여 직사각형 단면을 갖는 철근콘크리트 연속보의 최적설계 알고리즘을 유도하였고, 최적설계 프로그램을 개발하였다. 목적함수로서 건설경비는 콘크리트 경비, 철근 경비 그리고 거푸집 경비를 포함하였으며 이를 최소화하였다. 설계제약조건으로는 시방서상의 최대처짐제약, 휨 및 전단강도제약, 연성제약 그리고 설계변수에 대한 상·하한 제약을 고려하였다. 쿤-터커 필요조건을 이용하여 최적성 규준을 설계변수의 항으로 명시적으로 유도하였으며, 이때 설계변수로는 보의 유효깊이와 철근비를 취하였다. 구조물 자중의 영향을 실제 시스템의 평형방정식에서 고려하였다. 설계변수들의 개선을 위한 반복과정과 컴퓨터 프로그램을 개발하였으며, 수치예를 들어 개발된 기법의 적용성과 효율성을 보였다.