• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.215-228
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• 2007

By using the variational calculus of fractional order, one derives a Hamilton-Jacobi equation and a Lagrangian variational approach to the optimal control of one-dimensional fractional dynamics with fractional cost function. It is shown that these two methods are equivalent, as a result of the Lagrange's characteristics method (a new approach) for solving non linear fractional partial differential equations. The key of this results is the fractional Taylor's series $f(x+h)=E_{\alpha}(h^{\alpha}D^{\alpha})f(x)$ where $E_{\alpha}(.)$ is the Mittag-Leffler function.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.249-258
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• 1996

Analysis by the method of characteristics shows that if f and $u_0$ are smooth and $u_0$ has compact support, then the Hamilton-Jacobi equation $$ (H-J) ^{u_t + f(u_x) = 0, x \in R, t > 0, } _{u(x, 0) = u_0(x), x \in R, } $$ has a unique $C^1$ solution u on some maximal time interval $0 \leq t < T$ for which $lim_{t \to T}u(x, t) exists uniformly; but this limiting function is not continuously differentiable.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.287-290
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• 1995

Recently H$_{\infty}$ control theory for nonlinear systems based on the Hamilton-Jacobi inequality has been developed. In this paper, we apply the state feedback controller solved via Riccati equation to a semi-active suspension model, two degree of freedom vehicle model, and show that it is effective for vibration control..

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.411-418
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• 2004

Using a level set method we develop a shape optimization method applied to energy flow problems in steady state. The boundaries are implicitly represented by the level set function obtainable from the 'Hamilton-Jacobi type' equation with the 'Up-wind scheme.' The developed method defines a Lagrangian function for the constrained optimization. It minimizes a generalized compliance, satisfying the constraint of allowable volume through the variations of implicit boundary. During the optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian function. Compared with the established topology optimization method, the developed one has no numerical instability such as checkerboard problems and easy representation of topological shape variations.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.653-654
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• 2008

This paper presents a topological shape optimization for electromagnetic system using a level set method. The optimization is progressed by updating the implicit level set function from the Hamilton-Jacobi equation. The up-wind scheme is used for numerical implementation of the Hamilton-Jacobi equation. In order to validate the proposed optimization, the core part of a C-core actuator is optimized by three cases using different materials; (single steel), (two steels), and (steel and magnet).

• Proceedings of the KIEE Conference
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• 2008.10c
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• pp.23-25
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• 2008

This paper presents a topological shape optimization for electromagnetic system using a Level Set method. The optimization is progressed by updating the implicit Level Set function from the Hamilton-Jacobi equation. The up-wind scheme is used for numerical implementation of the Hamilton-Jacobi equation. In order to validate the proposed optimization, the core part of a C-core actuator is optimized by three cases using different materials; (single steel), (two steels), and (steel and magnet).

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.60-63
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• 1996

This study deals with the nonlinear H$_{\infty}$ control problem of linear system using nonlinear weight. Generally the solvable condition of nonlinear H$_{\infty}$ control problem is given by the Hamilton Jacobi equality or inequality, but it is very difficult to solve. In this study, some constraints of nonlinear weight reduce the solvable condition to linear Riccati equation. Some examples of the control system design using nonlinear weight are shown.n.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.412-415
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• 1995

Previously obtained results of L$_{2}$-gain and H$_{\infty}$ control via state feedback of nonlinear systems are extended to a class of nonlinear system with uncertainties. The required information about the uncertainties is that the uncertainties are bounded in Euclidian norm by known functions of the system state. The conditions are characterized in terms of the corresponding Hamilton-Jacobi equations or inequalities (HJEI). An algorithm for finding an approximate local solution of Hamilton-Jacobi equation is given. This results and algorithm are illustrated on a numerical example..

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.571-576
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• 2013

In this paper, we solve the optimal investment problem when the investor gets labor income and may have a wage increase. We assume the investor has constant absolute risk aversion(CARA) utility and obtain closed form solutions.