• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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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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• v.24 no.1_2
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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.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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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.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.3
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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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• v.4 no.1
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• pp.11-22
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• 1972

Determination of a two-point boundary value problem is the key of finding the control function u(t) with the application of the fundamental idea of Minimum principle. The late development shows the discovery of the initial costate vector for the solution of a two-point value problem. As a new technique of determining the optimal control function, Newton's Sequential method is examined about a number of engineering problems and found available.

• Nuclear Engineering and Technology
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• v.1 no.2
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• pp.79-85
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• 1969

Determination of a two-point boundary value problem is the key of finding the control function u(f) with the application of the fundamental idea of Minimum principle. The late development shows the discovery of the initial testate vector for the solution of a two-point value problem. As a new technique of determining the optimal control function, Newton's sequential method is examined in this paper.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.1
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.68 no.1
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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.