• 대한수학회보
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• 제53권5호
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• pp.1585-1596
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• 2016

In this paper we investigate the existence of nontrivial solutions for the following fractional boundary value problem (FBVP) $$\{_tD_T^{\alpha}(_0D_t^{\alpha}u(t))={\nabla}W(t,u(t)),\;t{\in}[0,T],\\u(0)=u(T)=0,$$ where ${\alpha}{\in}(1/2,1)$, $u{\in}{\mathbb{R}}^n$, $W{\in}C^1([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ and ${\nabla}W(t,u)$ is the gradient of W(t, u) at u. The novelty of this paper is that, when the nonlinearity W(t, u) involves a combination of superquadratic and subquadratic terms, under some suitable assumptions we show that (FBVP) possesses at least two nontrivial solutions. Recent results in the literature are generalized and significantly improved.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.231-243
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• 2007

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• 한국시뮬레이션학회논문지
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• 제2권1호
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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.

• 한국시뮬레이션학회:학술대회논문집
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• 한국시뮬레이션학회 1993년도 제3회 정기총회 및 추계학술발표회
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1150-1155
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• 1990

This paper proposes an optimal redundancy resolution of a kinematically redundant manipulator while considering homotopy classes. The necessary condition derived by minimizing an integral cost criterion results in a second-order differential equation. Also boundary conditions as well as the necessary condition are required to uniquely specify the solution. In the case of a cyclic task, we reformulate the periodic boundary value problem as a two point boundary value problem to find an initial joint velocity as many dimensions as the degrees of redundancy for given initial configuration. Initial conditions which provide desirable solutions are obtained by using the basis of the null projection operator. Finally, we show that the method can be used as a topological lifting method of nonhomotopic extremal solutions and also show the optimal solution with considering the manipulator dynamics.

• 전자공학회논문지B
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• 제29B권3호
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• pp.6-15
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• 1992

This paper proposes a method for the global optimization of redundancy over the whole task period for a kinematically redundant robot. The necessary conditions based on the calculus of variations for an integral type cost criterion result in a second-order differential equation. For a cyclic task, the periodic boundary conditions due to conservativity requirements are discussed. We refine the two-point boundary value problem to an initial value adjustment problem and suggest a numerical search method for providing the conservative global optimal solution using the gradient projection method. Since the initial joint velocity is parameterized with the number of the redundancy, we only search the parameter value in the space of as many dimensions as the number of degrees of redundancy. We show through numerical examples that multiple nonhomotopic extremal solutions and the generality of the proposed method by considering the dynamics of a robot.

• Nuclear Engineering and Technology
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• 제4권1호
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• pp.11-22
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• 1972

최대치(또는 최소치) 원리의 기본개념을 써서 제어함수 u(t)를 찾는데는 2점간 경계치 문제의 해결이 요구된다. 그런데 최근에는 2점간 문제를 푸는 방법으로 초기 costate vector를 찾아 문제를 해결하는 여러가지 편법이 개발되고 있다. 여기에서는 최적제어 함수를 찾는 새로운 방법의 하나로써 고안된 Newton's sequential방법을 써서 여러가지 공학적 문제를 풀어 봄으로써 이 방법이 매우 유효하다는 것을 알아냈다.

• Nuclear Engineering and Technology
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• 제1권2호
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• pp.79-85
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• 1969

최대치 (또는 최소치)원리의 기본개념을 써서 제어함수 u(t)를 찾는데는 2점간 경계치 문제의 해결이 요구된다. 그런데 최근에는 2점간 문제를 푸는 방법으로 초기 costate vector를 찾아 문제를 해결하는 여러 가지 편법이 개발되고 있다. 여기에서는 최적제어함수를 찾는 새로운 방법의 하나로써 Newton's Sequential 방법을 적용하였다. 그리고 일차적으로 주어진 문제의 수학적인 전개를 시도하였다. 앞으로 이 방법의 물리적인 의의와 공학적인 가치는 Computer에 의해서 여러 가지 응용문제를 해결함으로써 밝혀질 것이다.

• 대한산업공학회지
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• 제12권1호
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• pp.95-105
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• 1986

This paper presents an adaptive algorithm to generate a near-optimal closed-loop solution for a non-zero sum differential game by periodically updating the solutions of the two-point boundary-value problem. Applications to competitive advertising problem show that the adaptive algorithm can be used as an efficient tool to solve the differential game problem in which one player may take advantage of the other's non-optimal play.

• 전기학회논문지
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• 제68권1호
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• pp.129-139
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• 2019

In order for a gun-launched guided projectile to glide to the maximum range, when to deploy the fin and start flight with guidance and control should be considered in range optimization process. This study suggests a solution to the optimal guidance problem for flight range maximization of the flight model of a guided projectile in vertical plane considering the aerodynamic properties. After converting the nonlinear Multi-Phase Optimal Control Problem to Two-Point Boundary Value Problem, the optimized guidance command and the best fin deployment timing are calculated by the proposed numerical method. The optimization results of the multiple flight rounds with various initial velocity and launch angle indicate that determining specific launch condition incorporated with the guidance scheme is of importance in terms of mechanical energy consumption.