• Journal of Mechanical Science and Technology
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• v.15 no.10
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• pp.1356-1368
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• 2001

In this paper, the model reference adaptive control (MRAC) of a flexible structure is investigated. Any mechanically flexible structure is inherently distributed parameter in nature, so that its dynamics are described by a partial, rather than ordinary, differential equation. The MRAC problem is formulated as an initial value problem of coupled partial and ordinary differential equations in weak form. The well-posedness of the initial value problem is proved. The control law is derived by using the Lyapunov redesign method on an infinite dimensional filbert space. Uniform asymptotic stability of the closed loop system is established, and asymptotic tracking, i. e., convergence of the state-error to zero, is obtained. With an additional persistence of excitation condition for the reference model, parameter-error convergence to zero is also shown. Numerical simulations are provided.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

• 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.

• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.263-285
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• 2002

This paper presents a numerical procedure for solving initial-value problems using the special functions which belong to a class of Rvachev's basis functions $R_{bf}$ based on algebraic and trigonometric polynomials. Because of infinite derivability of these functions, derivatives of all orders, required by differential equation of the problem and initial conditions, are used directly in the numerical procedure. The accuracy and stability of the proposed numerical procedure are proved on an example of a single degree of freedom system. Critical time step was also determined. An algorithm for solving multiple degree of freedom systems by the collocation method was developed. Numerical results obtained by $R_{bf}$ functions are compared with exact solutions and results obtained by the most commonly used numerical procedures for solving initial-value problems.

• Kyungpook Mathematical Journal
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• v.30 no.1
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• pp.55-58
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• 1990

• Proceedings of the Korean Environmental Sciences Society Conference
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• 2003.11a
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• pp.27-32
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• 2003

Atmospheric and oceanic numerical models are usually initial-value and/or boundary-value problems. Change in either initial or boundary conditions leads to a variation of model solutions. Much of the predictability research has been done on the response of model behavior to an initial value perturbation. Less effort has been made on the response of model behavior to a boundary value perturbation. In this study, we use the latest version of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM3) to study the model uncertainty to tiny SST errors. The results show the urgency to investigate the second kind predictability problem for the climate models.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.2
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• pp.284-292
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• 2003

In this paper, we carried out the numerical examination of the initial value setting-up method to extend the range of optimal step parameter in a adaptive system which is controlled by LMS algorithm. For initial value setting-up methods, the general method which select the initial value randomly and the other method which applies the approximate value obtained from the direct method to initial value, were used. And then, we compared to the ranges of step parameter setting, the convergence speeds of mean-square-error, and the stabilities during the convergence process when the initial values were applied to the optimal directivity synthesis problem. According to the numerical simulation results, the initial value setting-up method by means of the direct method provides wider range for the step parameter, more efficient capability for convergence and stability, and more error correction ability than the general method.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.521-536
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• 2015

We investigate the nonlinear motions of discrete loaded cable with different periodic forcing. We present the numerical evidence of the nonlinear motions of the cable by solving initial value problems and obtaining the motions after a long time. There appeared to be various types of nonlinear oscillations over a wide range of frequencies and amplitudes for the periodic forcing term.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.137-147
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• 2022

In this paper, we considered the Dirichlet initial boundary value problem of a nonlinear viscoelastic wave equation with nonlinear damping and source terms, and investigated finite time blow-up phenomena of the solutions to the equation with arbitrary positive initial data, under suitable conditions.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.506-509
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• 2006

Extended Kalman Filter iterate the prediction and the filtering based on Initial state for the next time step. EKF method for the estimation of nonlinear parameters of a structural dynamic system is necessary that initial of state vector and error covariance matrix. Because those are unknown exactly, generally selected random values. That occasion observability problem appear because of unknown initial values. In this study, for the estimation of the nonlinear parameters, a simple one degree of Freedom example is carried out by Extended Kalman Filter. And initial value assumption for Parameter Estimation of Dynamic System are developed. The result of analysis is compared with calculated standard values.