• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.156-161
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• 1994

In this paper, we consider an optimal control problem of a nonlinear stochastic system. Dynamic programming approach is employed for the formulation of a stochastic optimal control problem. As an optimality condition, dynamic programming equation so called the Bellman equation is obtained, which seldom yields an analytical solution, even very difficult to solve numerically. We obtain the numerical solution of the Bellman equation using an algorithm based on the finite difference approximation and the contraction mapping method. Optimal controls are constructed through the solution process of the Bellman equation. We also construct a test case in order to investigate the actual performance of the algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.440-444
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• 1998

In this paper, we consider numerical solution of a H-J-B (Hamilton-Jacobi-Bellman) equation of elliptic type arising from the stochastic control problem. For the numerical solution of the equation, we take an approach involving contraction mapping and finite difference approximation. We choose the It(equation omitted) type stochastic differential equation as the dynamic system concerned. The numerical method of solution is validated computationally by using the constructed test case. Map of optimal controls is obtained through the numerical solution process of the equation. We also show how the method applies by taking a simple example of nonlinear spacecraft control.

• 대한수학회보
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• 제55권2호
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• pp.479-497
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• 2018

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.155-159
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• 1993

In this paper, we consider the problem of a stochastic optimal switching control, which can be applied to the control of a system with uncertain demand such as a control problem of a power plant. The dynamic programming method is applied for the formulation of the optimal control problem. We solve the system of Quasi-Variational Inequalities(QVI) using an algoritlim which involves the finite difference approximation and contraction mapping method. A mathematical example of the optimal switching control is constructed. The actual performance of the algorithm is also tested through the solution of the constructed example.

• 대한전기학회논문지
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• 제34권5호
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• pp.173-178
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• 1985

The control of a linear system with random coefficients is discussed here. The cost function is of a quadratic form and the random coefficients are assumed to be completely observable by the controller. Stochastic Process involved in the problem by the controller. Stochastic Process involved in the problem formulation is presented to be the unique strong solution to the corresponding stochastic differential equations. Condition for the optimal control is represented through the existence of solution to a Cauchy problem for the given nonlinear partial differential equation. The optimal control is shown to be a linear function of the states and a nonlinear function of random parameters.

• Journal of Electrical Engineering and Technology
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• 제9권1호
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• pp.80-89
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• 2014

A stochastic optimal power flow (S-OPF) model considering uncertainties of load and wind power is developed based on chance constrained programming (CCP). The difficulties in solving the model are the nonlinearity and probabilistic constraints. In this paper, a limit relaxation approach and an iterative learning control (ILC) method are implemented to solve the S-OPF model indirectly. The limit relaxation approach narrows the solution space by introducing regulatory factors, according to the relationship between the constraint equations and the optimization variables. The regulatory factors are designed by ILC method to ensure the optimality of final solution under a predefined confidence level. The optimization algorithm for S-OPF is completed based on the combination of limit relaxation and ILC and tested on the IEEE 14-bus system.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.85-97
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• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

• 한국시뮬레이션학회논문지
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• 제9권1호
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• pp.93-108
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• 2000

The stochastic manufacturing system has one or more random variables as inputs that lead to random outputs. Since the outputs are random, they can be considered only as estimates of the true characteristics of the system. These estimates could greatly differ from the corresponding real characteristics for the system. Multiple replications are necessary to get reliable information on the system and output data should be analyzed to get optimal solution. It requires too much computation time practically, In this paper a GA method, named Stochastic Genetic Algorithm(SGA) is proposed and tested to find the optimal solution fast and efficiently by reducing the number of replications.

• East Asian mathematical journal
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• 제34권1호
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• pp.1-16
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• 2018

We study an optimization problem for hyperbolic absolute risk aversion (HARA) utility function under two-factor Heston's stochastic volatility model. It is not possible to obtain an explicit solution because our financial market model is complicated. However, by using asymptotic analysis technique, we find the explicit forms of the approximations of the optimal value function and the optimal strategy for HARA utility function.

• 제어로봇시스템학회논문지
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• 제4권6호
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• pp.703-706
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• 1998

본 논문에서는 확률 최적 제어문제에서 발생되는 Elliptic type H-J-B(Hamilton-Jacobi-Bellman) 방정식에 대한 수치해를 구하였다. 수치해를 구하기 위하여 Contraction 사상 및 유한차분법을 이용하였으며, 시스템은 It/sub ∧/ 형태의 Stochastic 방정식으로 취하였다. 수치해는 수학적인 테스트 케이스를 설정하여 검증하였으며, 최적제어 Map을 방정식의 해를 구하면서 동시에 구하였다.