• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.99-112
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• 2012

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.367-385
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• 2001

In this paper, we characterize the smoothest density with prescribed moments. Hong and Kim(1995) proved the existence and uniqueness of such as density. we introduce the general optimal control problem and prove some theorems on the characterization of the minimizer using the optimal control problem techniques.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.3
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• pp.111-116
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• 2000

In this paper, we presented a new algebraic iterative algorithm for the optimal control of the nonlinear systems. The algorithm is based on tow steps. The first step transforms optimal control problem into a sequence of linear optimal control problem using the quasilinearization method. In the second step, TPB(two point boundary condition problem) is solved by algebraic equations instead of differential equations using BPF(block pulse functions). The proposed algorithm is simple and efficient in computation for the optimal control of nonlinear systems. In computer simulation, the algorithm was verified through the optimal control design of Van del pole system and Volterra Predatory-prey system.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.83-100
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• 2010

In this article, an optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier, the optimality system is obtained. The derived optimal system becomes coupled, non-symmetric partial differential equations. For discretizations and implementations, the finite element multigrid V-cycle is employed. The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.659-670
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• 2023

In this paper, we study the distributed optimal control problem of a coupled system of the host-pathogen model. The system consists of the density of the susceptible host, the density of the infected host, and the density of pathogen particles. Our main goal is to minimize the infected density and also to decrease the cost of the drugs administered. First, we prove the existence and uniqueness of solutions for the proposed problem. Then, the existence of the optimal control is established and necessary optimality conditions are also derived.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.108.3-108
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• 2001

In this work, we consider a real time optimal control problem of mechanical systems with restrictions for actuators i.e. input restrictions and constraints for the movable area i.e. state constraints. First, we formulate an optimal control problem which evaluates the cost function for a finite time horizon with input restrictions and state constraints of a wheeled vehicle as an example of mechanical systems. In this problem, the differentiability of the cost function is not required and this implies that the problem cannot be solved analytically. Therefore, in this work, we use an optimization method to solve the optimal control problem and a new real time optimization method is proposed to solve the problem. In this method, we provide a parameter that indicates the ...

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.247-259
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• 2003

Optimal control problem for the exploitaton of oil is investigated. The optimal control problem under consideration in this paper is governed by weak coupled parabolic PDEs and involves with pointwise state and control constraints. The properties of solution of the state equations and the continuous dependence of state functions on control functions are investigated in a suitable function space; existence of optimal solution of the optimal control problem is also proved.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.167-178
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• 1997

In this paper we present an application to airfoil design of an optimum design method based on optimal control theory. The method used here transforms the design problem by way of a change of variable into an optimal control problem for a distributed system with Neumann boundary control. This results in a set of variational inequalities which is solved by adding a penalty term to the differential equation. This si inturn solved by a finite element method.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.307-312
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• 1994

The authors have been devoted to researches on fuzzy theories and their applications, especially control theory and application problems, for recent years. In this paper, the authors present results on a comparison of optimal solutions between ones of an ordinary-typed mathematical linear programming problem(O.M.I.P. problem) and ones of a Zimmerman-typed fuzzy mathematical linear programming problem (F.M.L.P. problem), and comment about the sensitivity (differences and fuzziness on between O.M.L.P. problem and F.M.L.P. problem) on optimal solutions of these mathematical linear programming problems.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.4
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• pp.198-204
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• 2003

In this paper, we presented a new algebraic iterative algorithm for the optimal control of the nonlinear systems. The algorithm is based on two steps. The first step transforms nonlinear optimal control problem into a sequence of linear optimal control problem using the quasilinearization method. In the second step, TPBCP(two point boundary condition problem) is solved by algebraic equations instead of differential equations using the new integral operational matrix of BPF(block pulse functions). The proposed algorithm is simple and efficient in computation for the optimal control of nonlinear systems and is less error value than that by the conventional matrix. In computer simulation, the algorithm was verified through the optimal control design of synchronous machine connected to an infinite bus.